Never got to play these PS1 experiments, but I was curious about them, too. I am a big Contra fan, though.
I haven't played Uprising because it somehow just didn't seem to be "Contra" enough from the trailers. You've had a good taste of Contra with Super C, which is a fun, quality entry. (I go back and forth on whether Super C or its predecessor, the self-titled Contra, is the better NES entry). Contra III: The Alien Wars is arguably the best Contra game to date. Operation C and Contra 4 are also top-of-the-line, excellent Contra entries. (Contra 4 was a DS system seller for me). Hard Corps is very interesting, but I never got to play through the whole game as I had the Super Nintendo and not the Genesis, so I can't give a final review. (However, it's worth mentioning that III and Hard Corps are usually considered the contenders for top Contra). Contra: Shattered Soldier is a solid entry, but a little stilted in level design; also, it feels like it played it safe and conservative in some respects. (Contra 4 has that latter issue a bit, playing it safe, which is its biggest flaw, but nonetheless feels more fluid and fun in process). Neo Contra is super experimental, highly underrated, and a lot of fun (it feels like an early prototype of what Contra in 3D could be in some of its basics).
I don't think any game, including Vanquish, has captured a Contra in 3D feel; though, Gears of War is a definite no-no. Contra needs to be fast and fluid. It almost needs motion-control aiming and firing while you move the character with a stick to deal with the frenetic attacks from all angles and free up the ability to jump. That's a daring route that won't be tried, but I think would serve the series best. Go big or go home. Contra always has to be over-the-top.