My preferred console is the 360, but that doesn't necessarily mean that it's the superior nor does it mean it's my pick out of the two.
If there is a game that's available on both platforms--a 3rd party tittle in other words--then I'll go for the 360. I prefer the achievement system as opposed er to the trophy system, I like being able to set up a party/private chat with friends, the online community is larger, and the majority of games are better supported meaning earlier content. It's just a lot more community friendly if you like online play and interaction. I also enjoy the layout of the dashboard on the 360; I'd said it's more user friendly, things our easier to find and it tends to be quicker to navigate.
However the biggest shortcoming of the 360 is the lack of exclusives; there just isn't enough, and definitely not enough time quality ones - this has always been Microsoft's problem and its still present. The PS3 on the other hand excels in this department -- it has the best, in terms of quality and quantity, across all the platforms of the 7th generation by a mile. So if I had to pick one I'd easily pick the PS3 just because it offers more in terms of quality games, I'd only choose the 360 when there's a 3rd party title. I also like some of the features on the PS3: Internet browser (it was originally exclusive), blu-ray player, PS Home (free and actually really fun), PS plus etc. The design of the PS3 itself--the actual console I mean--Is slick and stylish.
I guess it comes down to your preferences though. I'm not a big JRPG fan but I'm pretty sure the PS3 has quite a lot of popular exclusive games within this genre. On the adventure side you have games like The Last of Us, all three games from the Uncharted series, the Rachet and Clank games, God of War (slightly adventure based). I couldn't give you suggestions on the other two as I'm not exactly interested in those genres, but the fact remains, PS3 simply has a ton of quality exclusives.
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Overall I'd recommend the PS3, it offers so much more in terms of games and the Xbox only wins when you're dealing with 3rd party online titles and even then it's not a huge difference between the two.