3ds

[New] 3DS [XL]. It's the best console this gen anyway with some of the greatest games this gen, including Fire Emblem Awakening, 3D Land, Resident Evil Revelations, Kid Icarus Uprising, Luigi's Mansion 2, Animal Crossing New Leaf, Mario Kart 7, Zelda OOT, MM & ALBW, Kirby Triple Deluxe, Monster Hunter 3&4, Rayman Origins ect ect ect.

Really depends which kinds of games you like

Go with the 3DS ...

Buy both, because otherwise you will miss out on some nice stuff. And please do not buy a 2DS, you should get a new 3DS (XL or not depends on you, but I really recommend the new one).

3DS: Bravely Default, (Bravely Second - western released not confirmed yet) (RPG) , Etrian Odyssey Untold: The Millennium Girl (Dungeon Crawler) , Fantasy Life (RPG) , Fire Emblem Awakening (Fire Emblem If) (Tactics RPG) , The Legend of Zelda (Ocarina of Time, Majora's Mask, A Link Between Worlds) (Adventure) , Mario Kart 7 (Racer) , Monster Hunter 4 Ultimate (Action RPG..?) Ace Attorney Games (1-2-3, Dual Destinies) (Adventure VAs) , Pokemon X/Y R/S (RPG) , AA vs Professor Layton (Puzzle VA?), Shin Megami Tensei 4 (RPG) , Star Fox 64 3D (On rail shooter) , Super Smash Bros (Fighter)

Vita: Atelier Games Rorona/Totori/Meruru/Ayesha (RPG) , Blaz Blu (Fighter) , Danganronpa games (VA) , Disgaea 3/4 (Tactics RPG) , Dragon's Crown (Arcade Beat 'Em Up) , Hotshots Golf (Sports), FF10-X2 (RPG) , Freedom Wars (MH style game?) , God Eater 2 (MH gane?) , Gravity Daze (Action?) , Hatsune Miku Project Diva 1-2 (Music Rhythm games) , Hyperdimension Neptunia games (RPG?) , Lego Games (???) , Minecraft , Muramasa Rebirth (Platformer?) , Persona 4 Golden (RPG) , Soul Sacrifice (MH game?) , Tales of games (RPG) , Uncharted Golden Abyss (Adventure), PS plus games if you have PS plus.

Feel free to add to the list if I missed any, or recommend one.

I use my vita for remote play DAILY. Ignore jay's comment about it ...

Many games have thier controls adjusted when in RP (i think he's a self proclaimed MS fanboy anyways). Other than that, you just need to adjust your controls in game (like I did for BL2 today), or firmware if necessary.

In terms of games, I only play ps+ and remote play - but that's more than worth the cost.

I would go with PS Vita though 3DS is also very awesome imo!
PS Vita has the games which I am more interested in (Uncharted, Killzone, LittleBigPlanet, Tearaway, Gravity Rush, Soul Sacrifice, Freedom Wars, Metal Gear Solid, Final Fantasy, Ratchet & Clank, Sly Cooper, Jak & Daxter, God of War, Minecraft, Playstation All-Stars, Street Fighter x Tekken, Borderlands, Persona, Need for Speed, Fifa, Assassin's Creed, Call of Duty, Toukiden, Tales of, Sword Art Online, Rayman, Dangan-Ronpa, Mortal Kombat, a lot Japanese games and PS1 / PSP games. PS Vita also have Remote-Play and Playstation Now. And PS Vita is more progressive than 3DS and is very very very high-quality. And you are Mr.Playstation, you will love PS Vita!

I would get the 3ds first since it will take you months (even years) to make your way through all the amazing titles. But it should be on your list sometime to get a Vita. I scoffed at first, but it's actually become one of my favorite gaming devices ever. And that OLED screen (unless you get the Slim) is so luscious.

In the end, like everyone said, it comes down to which games you like best. Vita = RPG heaven. 3ds = Nintendo games (you already know them all).

Honestly the Vita is dead, you will be buying it just for games that have already come out plus the trickle of Japanese games here and there. If you like the games that have been released already then get it but there wont be any more games like Uncharted or Killzone on it.
Just wait till its bargain bin price.

The 3DS has the greater library but weaker specs. BUT it will still be getting new games periodically. It holds a lot more value than the Vita in that aspect.