I find it hard to recommend Croixleur. It's not bad, but to me it really didn't feel like there was much of it and I could feel myself getting bored with it fairly quickly.
There's someone from Nyu Media on GAF who I think would be pretty handy to have in this thread.
You probably mean me, who always lurks GAF like a cyborg-ninja. Dem nanomachines.
Anyway, Croixleur is more like Blood Palace from Devil May Cry. It is objective based as well, as in besides the main story goal of clearing the tower (don't wanna spoil but there is a bit more to it) you have a collection of medals that have certain requirements and also a plethora of weapons at your disposal (some to deal with air threats, others for ground and others multi-purpose) for both of the characters. You also kind of keep a combo chain going through the floors of the tower (which is reset if you get hit) so there is a fine balance between risking to get damaged, landing hits, knowing the enemies, knowing when to cancel-out an attack by dashing or attempting to parry a move with your sword. (Although you just strike back instead of performing a riposte ala Dark Souls.) There is also a 2-player test mode, called Dramatic Battle, but unfortunately it's only local. Maybe for the sequel (if it happens) extra depth can be added.
I enjoyed the Time Attack mode best outside of story mode because it keeps you on the edge, comboing and chaining like mad against the clock.
Surprised that Steam didn't throw Fairy Bloom Freesia, the other game by Edelweiss (and my personal favourite). It's more a brawler than a beat 'em up, very, very colourful as well and with a deeeeeeep moveset and combos chaining galore as enemies will crash into each other leading to massive combo chains that you can keep up for extreme badassery. In fact, I think someone at GAF made a gif of that kind of comboing. Hell, advanced comboing in Croixleur also looks badass but perhaps not as flashy as Freesia.
Fairy Bloom Freesia:
http://store.steampowered.com/app/214590
Oh, speaking of Crimzon Clover, Danmaku Unlimited 2 is also on Steam and it's freaking awesome as well. Both definitely very ship oriented. In a different vein, you have eXceed 3rd but that enters what can be described as "waifu territory", right? eXceed 3rd was apparently meant to be played in its hardest setting, without auto-bomb in order to face the hidden boss, which in the end leads to a final, secret extra stage that's... Well, it's quite something. You can unlock the secret boss in other difficulties too.
Danmaku Unlimted 2:
http://store.steampowered.com/app/280560/
eXceed 3rd:
http://store.steampowered.com/app/207400/ (Just ignored the silly name, gotta love Japan for that

I mean, at least it's not called Egocentric Embroiders, right? There is a doujin game called like that btw.)
OH! And someone mentioned Brothers: A Tale of Two Sons, right? I have another 3D game kind of like that (well, because it's also made in Unreal Engine) and that's Papo & Yo. A fantastic, if a bit short game with some nice and strange touches. Easy to clear for the busy people like me!
http://store.steampowered.com/app/227080/
And someone looking for a good puzzler, and I mean a really challenging and interesting one, try LYNE! GAF hyped this to me and I silently bought it. Loved every bit of it:
http://store.steampowered.com/app/214590/
Another vote for Hard Reset too. Hell, I need to go back to it now that I have a PC that can handle it at the highest settings. The comic-book style of the cutscenes is pretty damn awesome too.
edit: seeing it's in a Groupees bundle, while it has its flaws (namely, that it tries to be two different genres at the same time without excelling in neither and some save issues I faced upon release),
Ballpoint Universe is something
unique. Seriously, I just love that art style and the shmupping (while no Crimzon Clover) was decent enough, just nowhere near as epic as the art style could've allowed. The final battle was nice though. Seriously, give it a try!