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.