Since the listing page was already long the opinions are better in a new one.
Exceptional games
Geometry Wars - This is one of the best shooters of all time, and all its iterations have been awesome. The one I enjoy most is Geometry Wars: Galaxies (Wii) and I have them all except the ones inside Project Gotham Racing games (2 and 4). Even if it's not my favorite, Geometry Wars 3: Dimensions is still an awesome game. The most striking feature of the game is its simplicity, it's just a no-frills shooter but an exceptional one. There are several original modes in this version, and the hardest and that I really don't like, but have to admit it's clever, it's Pacifism. The Pacifism levels are by far the most troublesome ones to master and to get the 3 stars. Still, it's an absolutely essential title to any person who likes shooters. It's digital-only, available on the PS4, PS3 and Vita and has completely separate but similar trophy lists for the 3 games. The Vita version is a particularly extraordinary feat as it feels almost like the PS3 and PS4 versions, and it's not screen clipped due to the lower resolution. It's not a perfect game. Do expect spawns over your ship, and sometimes the collision detection is not stellar. Totally unmissable.
Assault Android Cactus - An exceptionally fun shooter with a charming plot, characters and enemies and is so eminently playable. Good sound and music, good graphics, fluid controls, simplicity, everything you could want in a shooter. It borrows the keep the chain mechanic from Ikaruga. The game is extremely hard due to this and lots of RNG in the waves spawn points and movements, as finishing the levels isn't hard, but maintaining the chain to the end is. It was supposed to have a Vita version, but I doubt it could have been a decent game. Should not be missed either.
Dead Nation - This is the best Housemarque game by far (unfortunately, I'll get back to this). A good and well-thought campaign with no RNG so you can master all its aspects. Fluid gameplay and good progression. Nice and varied weapons, and you can upgrade the ones you want and not the crap that RNG will provide. Good enemies, are introduced along the way and along your character progression. Good atmosphere. And then a stupid and pointless DLC, Road of Devastation, which has some good ideas but it's so plagued by RNG that it's a mess. Probably created for the complainers that the main game is always the same. Still, the game itself is exceptional, particularly in morbid difficulty. Undead is not much worse than morbid, you'll only probably get out of ammo quicker. It's digital-only, available on the PS4, PS3 and Vita and has completely separate but similar trophy lists for the 3 games. The Vita version is awesome, although it has a few drawbacks but not in gameplay. Another sure one to have.
Good games
Alienation - I don't really know if this one should be here or in the regular ones. It's a absolute heartbreaking disappointment. Here is the most exceptional shooter in terms of gameplay, graphics and sound only to be smashed to pieces by RNG. There are some amazing enemies. The graphics are awesome, from the alien artifacts to the clever ice and light effects (check the light once you get out of the barracks near the house with the huge cannon). Music and sound effects are top-notch. But this game is a plain RNG bore, totally the opposite of Dead Nation. The maps are always the same, but enemy groups and particularly bosses appearance and placement are random, so you can have at any difficulty runs that are a walk in the park or a nightmare. As an example while I was trying one of the characters in World 1, in the first mission I had 6 bosses in my path to finish it and I could only avoid one. If I was a new player I would probably never touch the game again. This is why RNG (or the pointless "procedural" glorified RNG) is a dumb option. To make it even worse you can get the best weapons for killing a meaningless member of a mob, and absolute junk ones after a huge battle with a boss, so there is almost surely no reward for doing the most difficult jobs in the highest difficulties, another baffling decision. There's no sense of progress, receiving as level end prize in legend 6 weapons all uncommon and common ones it's bloody stupid. And in the end the game is too easy, even in Legend difficulty, although granted the game is much better and interesting on master and legend. If there wasn't a bloody mess of RNG and design decisions, Alienation would be by far the BEST available shooter. And then Housemarque boss complains that arcade is dead. Of course it is, and they did their share to bury it. I'll come back to this... What an absolute waste.
PixelJunk Shooter 1 / 2 / Ultimate - This is an interesting game, but not really a true shooter. More an exploration, puzzle and shooter mix. The cartoonish pastel graphics are interesting, and the fluids and lights pseudo physics are nicely done and convincing. The bosses are interesting. Interesting homage to Dig Dug (doesn't work very well...) and Galaga in one of the stages. The ultimate version is an update for the PS4 and Vita containing the original 1 and 2 games from the PS3. The Vita version does suffer a lot from the reduced screen area but can be done, although it's harder than the PS4 version (except on the final bonus mission where it's easier on the Vita). It's a good introduction to shooters as it's less difficult than most other ones. Cross-buy, cross-save and cross-play.
Neon Chrome - This game has a difficult and obtrusive start. I did struggle to really figure out how the hell to play it. Once you get over that it's a good shooter and one of the only games where RNG levels (okay, not RNG, procedural...😂) do work and don't make a mess. There are some interesting weapons, some nice perks (and you can buy some at the level start to reduce RNG), the smart use of color helps the game a lot, the sound and music are good and gameplay is fluid. The only downside is crappy RNG to get some bonus levels, but 10Tons are the kings of RNG. Still, it's a quite good shooter overall. Don't miss doing the boss levels with the crossbow. It's also good for starters as you can farm power to make it easier if you need it.
Jydge - The best 10Tons shooter overall. Interesting missions, with some puzzles thrown at the mix, which makes it reasonably original. Very similar to Neon Chrome in many things, but maps are not RNG generated. Good cyberpunk atmosphere and music. Satisfying gameplay and not terribly hard. Recommended.
Prismatic Solid - I'm always fond of one-man shows, so I give these some greater respect. This game is the child of a solo Japanese programmer, who clearly is very good at 3D work. Although the game is mostly a 2D shooter, the enemies and environments are 3D objects generated in real-time. So it's particularly unique (Geometry Wars has sprites...). It has a lot of interesting ideas, good gameplay and good music. Being so different from everything else it's quite recommended.
Regular games
Nex Machina - Oh boy... This game has some exceptional roots. Robotron is one of the best shooters of all time, again for keeping a sound idea simple. There are no frills in it, but the game simply works and it's mighty fun to play. Nex Machina being its spiritual successor made the fatal mistake of precisely killing that: the simplicity. The graphics are exceptional, the effects too, sound and music are top notch. But then begin the issues. Hum, it's a Housemarque game, let me take a few wild guesses. It has a dash ability? Check. It has a secondary weapon? Check. It has a power-up? Check (well Dead Nation doesn't 😋). The main problem with Housemarque is that fundamentally all their games had the same core mechanics, and the only one where it really works is Dead Nation, and the other that could have is Alienation if they did not make a mess. There was little variation or innovation in their games, which sometimes it's not necessary anyway as long as the final product is good. Nex Machina is too complex and sacrifices Robotron's simplicity to gain... nothing. It's difficult to say what kind of shooter even is, as it ranges from bullet hell to quests to puzzles to whatever is next but ultimately the plain good shooting experience seems to be there but it's not. Unfortunately disappointing, it's fun but nothing stellar.
Ruiner - I was really anticipating something extraordinary by reading the reviews and comments on this game. Surely come out disappointed. For starters what really is cyberpunk design has some latitude. But Ruiner developers used that to just make things dark and hide them which isn't helpful or even practical in this case. The game has a ton of pointless stuff, like the main hub (finding cats?!?!?) and the light speed bike. Smartly the game uses all buttons on the controller, and quite a few for more than 1 function, which is a mess in a shooter (all really good shooters just happen to be awesome with 1 or 2 buttons besides directional controls...) and probably they were pissed the controller didn't have a few more to use. Then there's the combat which is the biggest mess. Enemies have no patterns or anything discernible they just spawn and attack. Bosses are just worse versions of this with one that just randomly teleports around randomly. I can't even understand if they wanted to give a Dark Souls combat feel or anything else. Bosses are also bullet sponges (and supposedly they're better after patches), but in the end before these patches you could also cheese all bosses by using some abilities, which was bloody stupid. They tried to apply every single idea they probably had or seen in every game they played and the result is a bloody mess, as there's really nothing that is stellar in the whole game. It's playable, but what a fraud.
Super Stardust Delta - This Asteroids evolution on a 3D planet is an interesting shooter. There are 3 main weapons, that work in original ways. The graphics and sound are good, and it's enjoyable to play. However, there's a lot of RNG in a few things you'll want and it becomes annoying: the shields are RNG, the weapon upgrades are RNG. Collision detection is already a thorny science in 2D, in 3D is a lot worse and it will show, both for your benefit and prejudice. However, the biggest issue was that they decided on the Vita version to have minigames with touch and even worse motion controls. And trophies on those games. Either because Sony decided to cut costs and chose cheap and crappy touch and motion chips and sensors, or they were uncharted territory at Vita creation time, the simple fact is that these things don't work properly in the Vita. So anything related should be in the try for fun department and not on the you'll likely have to do it one. Because at that moment the game sucks badly, it's imprecise and annoying. And then the fun is gone.
Weak games
Tesla vs Lovecraft - This game starts so well. An interesting shooter, with some good mechanics, use of color, fluid gameplay, good sound and music. Progress is good until you get to Eldritch difficulty, the highest one. Then the game becomes a boredom fest of stupid RNG as around 25% of the missions are simply impossible unless you get the right perks. Which are random... There's no true skill involved, you simply can't do the missions without upgrades that will help, so it's playing until RNGesus will provide a decent combination that can make the levels playable. A bloody stupid decision that ruined an otherwise good game. Let's face it RNG does simplify a lot of things in development, and 10Tons does abuse that with the expected results. Avoid.
Wanted Corp. - For starters, I must say I only finished the Vita version. The game isn't dreadful, but it's quite dumb. You play with an AI partner that is totally dumb. The color scheme used doesn't work, as it's a sort of Dead Nation one tone maps, but it's mostly confusing and you can't see anything decently. In the Vita version, you're hit by enemies outside the screen, which are probably remains from the PS3 version which likely has twice the screen size. Bosses are a joke to deal with. The story is as dumb as possible, and the dialogs are laughable. The best thing overall is an AI partner that says that you have to be careful with mines and throws itself to them one or 2 secs later...
Tachyon Project - A interesting Geometry Wars clone with a few good ideas, but too many bugs and issues. Also too easy. Seems to be a rushed or unfinished project. A pity, had potential.
Dreadful games