I played it through on the PS3, and FFXIII looked absolutely beautiful on it. I also own it on my 360, but I've yet to play it. I'm sure the differences between the PS3 and 360 versions aren't dramatic either way.
If you really liked all of the other Final Fantasy games, then I don't think it'd hurt too much to give this one a go. It's very different to what you might be used to, however. The game is very linear, even when the world opens up for you to explore. Battles can sometimes get really boring as all you do really is hit the action button and switch paradigms, so long hours of grinding or farming later feel more of a chore than anything else.
What the game does have is a pretty good story backed up with breathtaking visuals. The characters are well designed and likeable too - even Hope after a certain point if you become frustrated with him at the start. A lot of people disagree with me, but I really enjoyed the levelling up system too. It is, like many aspects of the game, linear but each character you build only take on certain attributes at certain tiers and trees, or not at all. Each character is still better than an other at certain things.
If you do decide to go for it, you then have the console to pick. Like I mentioned, I doubt there being any huge differences between the two. If you really like the older Final Fantasy games, you might want to consider a PS3, as you can download V, VI, VII, VIII and IX from the Playstation Store. If you manage to get a pre-owned 60GB, you can also play X and XII on it because it's backwards compatible. Plus, the PS3 has some pretty good exclusives like LittleBIGPlanet, Uncharted, Killzone, White Knight Chronicles and Heavy Rain.
360's are cheaper, but you'll miss out on the possibility of owning and playing the previous Final Fantasy games, and definitely Final Fantasy Versus XIII in the future. The 360 has some decent RPG exclusives such as Lost Odyssey and Fable, and other games such as Halo and Gears of War.
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