Nice. I forgot about Federation Force (mostly I just remember the controversy with it not being what fans expected or something), but I have never heard of either of the others. I will have to look into them.
The 3DS has such a wide range of genres (although it is heavily biased toward RPGs and Platformers) that I’m not surprised there are more than one FPS for it. Wasn’t there one called Ironfall? Or was that one was 3rd person?
Unless you consider Ace Combat an FPS, the 3DS doesn’t really have any of them that I know of. You’d be better off playing the old DS ones. If you count Homebrew, your options expand a lot. Doom and Quake play wonderfully on the New3DS with the C nub.
As far as my favorite games on it: wow, there are so many. Shin Megami Tensei IV (and Apocalypse), Fire Emblem Birthright, Animal Crossing New Leaf, Pokémon, Monster Hunter 4U. The list goes on.
Looking at some screenshots, that may have been Dementium Remastered as mentioned above by SturgiesYrFase. I’m not sure if it got a demo, and I hadn’t heard of it until about an hour ago, but it’s a guess.