Reason 1: If your a Smash Bros. fan then you can get Super Smash Bros. 3D and play it all the way up until the WII U release. Not to mention it seems that the 3DS version is going to have content that the WII U won't. That's of course just speculation for now.
Reason 2: A PSP Vita breaks far more easily. I'm sorry Vita, I love you but you're just not as sturdy as a 3DS. I don't know if it's a big reason for you but if you're accident prone like me then you want something that's built to last.
Reason 3: More current games. Sure, the Vita still has a few titles coming out if you look hard enough. However, it's not slewing out as many as the 3DS is. This is my third reason listed since it isn't a big reason, but I don't like to buy expensive things if I'm not going to use them often.
Well I think that the two are very evenly matched, but here's three points that the Vita just can't offer:
It's a lot more portable than the Vita. The box-like 3Ds can easily fold and fit into tight spaces, and maybe even your pocket, along with a few games! On the other hand, the Vita feels very clunky with the controls sticking out .
There's a lot more games available. If you get bored, you can just go out and pick up a new one. Lots of good games out there, waiting to be discovered.
I like the overall usability of the 3DS. The controls are simple yet fun to play, and it powers off or sleeps at the click of a button.
I don't think I can give you three reasons to choose the 3DS over the Vita, as I haven't experienced the Vita myself, however, I will tell you what I enjoy about the 3DS.
Let's be honest, Nintendo is the leading company when it comes to handheld games, and for good reason. They've got a swarm of interesting, inventive, unique games that you just don't see elsewhere. You've got amazing RPG's like Bravely Default, Fantasy Life, Fire Emblem, ShinMega and many more. If RPG isn't your thing, there's plenty of puzzling, adventure games to get into like the Professor Layton or Phoenix Wright Series'. Virtue's last reward was one of my favourite puzzle/adventure games, but I think Vita gets that as well. There's also a lot of interesting fighting/racing games, not to mention all of the exclusives that make Nintendo what it is, like Mario Kart, Smash Bros, Animal Crossing, Super Mario, Kirby, Pit and way more.
Price wise, the games can be a little steep. Depending on where you live, you could end up payying between £20- £40 on a new game, but pretty much every game you can purchase in store, you can also purchase from the eshop, or online. Purchasing download codes online tends to be the cheaper option, it's what I do, and I save a lot of money by doing it.
3DS isn't a powerhouse of games, 3DS is a powerhouse of brand name whoring. Vita has the better games stuff like tearaway, gravity rush, Soul sacrifice, most of the console fighting games, killzone, rachet and clank, sly all the psp and psone games on psn.
If you want games vita is the better choice, if you want brand names 3DS is. Also vita has better controls, better hardware, better screen, better multimedia features and better everything else except camera then 3DS. The games on vita look and play better and can be far more advanced.
I wouldn't recommend it. Nintendo screwed me over with region locking and really high prices for games. This is the only time in my life when I thought a company deserved piracy. With the Gateway support for the new firmware coming up, I recommend pirating it to hell.