Give me some good reasons why this is better than that.

Vita
5" OLED display
Better grafix
Better online and social networking
Twitter
Flickr

Facebook

X game chat

and biggest reason:

Better games for me

3DS wins this one pretty easily.
3DS has a better software and a brighter future.
3DS'Circle Pad >>>> Vita's Analogue Stick(s).
3D is an interesting feature. Way more than anyone will admit. For games and videos.

The above ( by Turkish) and also: 

No region lock ( excellent for those who import games)

Multi-touch (front and rear),

PlayStation Plus (Instant game collection),

Cutting edge technology in a dedicated handheld Console,

Sony Ip´s,

True Dual analog sticks (no circle pad or something like PSP)

Different gaming experience on the go and also adapted console gaming to a portable experience language.

PSV.

Why? Psn is the best service of a handled. Minimum a game to month

This thread hasn't erupted yet; I'm glad for that.

I've only played a few 3DS games, and I haven't yet played my Vita, but I think at the moment the better investment is 3DS. It's less expensive, has backward compatibility, it has a bigger and better library of games (of course this all relies on taste), it provides access to classic Game Boy games, and, as MattyPeq said, its future is brighter.

Ultimately it's all about your taste in games. If you genuinely love the software for Vita, it will be the better option. But I would recommend waiting a bit for a hardware price cut, or at least a price cut for memory cards.

3DS games look almost like the Vita(to me), has more games than the Vita, more users than the Vita (great for street pass, not so great for the generic near j/k), better online community than the Vita, fully backward compatibility with your regular 3DS games, equivalent if not better features than the Vita, it has NINTENDO GAMES compared to the Vita, games are more diverse and more fun than the Vita and *DRUM ROLLS* :

it probably has a better future (less chance of being d/c) than the Vita due to the inability of the Vita to sell to consumers.(thus better 3rd party support in addition to Nintendo exclusive IPs)

It depends, do you like Nintendo games? If so, get a 3DS, if not go for a Vita

fixed ;P Since 3DS is not all about Nintendo games seeing that it has great 3rd party support as well.

3DS XL has just released a Pikachu edition. I also have the Legend of Zelda limited edition 3DS. These points alone mean that 3DS is ten times more awesome than the Vita.