If you're looking for games that will keep you entertained for 1 hour+ sessions and in bed, at home. The Vita is the choice for you.
If you're interested in mostly shovel-ware and a few decent titles to play in your 5 minute downtime on the crapper, the 3DS is the way to go. Oh, and there's Pokemon X and Y coming out later this year.
The 3DS and Vita are
VERY different platform with
VERY different target audiences. Take a very good look at the games lineup of both handhelds and make your choice wisely. For me, personally, the Vita trumps the 3ds in every department. The only thing it lacked was some decent JRPGs, very well fixed by Atelier Totori, Atelier Meruru and Soul Sacrifice. (If you never played an Atelier game I highly recommend them!)
I have both, personally, and love my Vita to death. Love it and the games it has, though I speak Japanese and have full access to all the games in the Vita library. I only wait for English versions of games I know are getting them.
Most people would have you believe that the Vita's library is small or not as good as the 3DS. This isn't true if you discount all the shovel-ware stuff the DS and 3DS are notorious for. If you never had a PSP or PS1 then playing those old games on the Vita is worth it for the OLED screen, if did have a PSP/PS1 then it's a good way to breath new life into those games. Here's a list of all PSP, minis and PS1 games that work on the Vita.
http://www.cheapassgamer.com/forums/showthread.php?t=316058
Also, the Vita is region free which is a godsend for me that imports games regularly. I can't play any of the Japanese library that I want to play on the 3DS because I refuse to shell out for both an NA and JP 3DS. This is a major downfall to me, but probably not for most people, I admit.
Absolutely look into PS+ if you do buy a Vita. The amount of free games you will get in the first month of subscribing will offset not only your memory card but also your subscription fee. If you have a PS3, then you will be blown away by the freebies. It looks like the Vita will be pushing its cross play feature with the PS4 to new levels as well, which will be really interesting to see.