I've flip-flopped a bit this gen. I got both my PS3 and 360 within months of each other and for a very long time, the 360 was my favourite. It was the one I had access to all the time and most of my friends had one, so we'd play a lot of things together. I would generally buy all the cross-platform games on 360 for achievements and because pretty much all my games were on there.
I got really disillusioned with my 360 once it RRoD'd; when they sent it back, the new one had a big scratch on it from the get-go. It was already a hassle to send it in (they made me ship it myself instead of sending a box like I'd been led to believe they would do) so I just kept it but I didn't really want to play it from then on. The dashboard for the 360 has also just gotten worse and worse over the years, though, and eventually it got so bad that I just couldn't stand turning on the console only to be bombarded with ads everywhere. When the ads are bigger than the button for "play the game in the disc drive" icon, you know there's a problem. By then we'd started drifting away/getting bored of our 360 staples so I stopped paying for Gold. And that's probably the best gaming decision I've made in a really long time, because even with Gold I was still subjected to those same ads that the silver/basic users get. I had to deal with the dashboard that catered to the US instead of Canada (we didn't have nearly the same music/TV/movie/media selection as the US), and it's not like anything worked out of the box without Gold anyway--without it, you can't watch Netflix (a service I already pay for) or use any of the extra apps they always advertise. (Gold also doesn't go on sale here nearly as much as it does in the US... or it didn't at the time anyway, so $60/year? No way.)
Around that time, I started going through my PS3 backlog and realizing just how great a console it was. No, it doesn't have the voice chat that I'd really liked on the 360 but hey, the 360 doesn't even have that if you aren't willing to pay their ridiculous XBL fees so it's not like that's really a big deal. Then that whole fiasco with PSN accounts getting hacked occurred and I thought Sony handled it brilliantly. I wasn't even affected and I still got a handful of free games. I started playing my PS3 more and more and when I moved into my current house, my roommate had a PS3 Slim so I didn't have to give up playing when I went away for school. I wasn't on board with Playstation Plus when it first came out, but within a few months (ie as soon as they announced Vita support)? Yeah, I upgraded to that. I pay about as much per year as I did for XBL except I actually get free games and great discounts. I'm not bombarded with ads whenever I turn on my console, I don't have to pay to use Netflix, and I just feel so much more comfortable as a consumer on the PS3. It's easy to find everything I'm looking for and the overall quality of the service is just so much better, in my opinion. I've heard the online crowd is much saner, too, but it's also much less saturated (I'd imagine) so of course it'll be quieter. :/
The other day I even sat down and took a look at all my Xbox games. The only game on 360 I'd be sad to have missed that I wouldn't have been able to play had I gone PS3-only was Beautiful Katamari and, honestly, that wasn't even too great a game. Literally every other game I liked on 360 came out on PS3 at some point and if not on PS3, the game was much better on PC. (So for example: Left 4 Dead, despite not being on PS3, is just disappointing to go back to on 360 now.) Halo did nothing for me, I absolutely dread going back to Gears of War 3 with my roommate even though we're almost done the series... and I just... didn't like anything on 360. It was doing well with indie games and XBLA but now it's impossible to find anything new on the dashboard unless you know EXACTLY what you're looking for. Even then, good luck figuring out how to do it if you only check the console once in a while.
Favourite games, though... I guess I'll only mention exclusives. I already said that the only 360 exclusive I would miss if I didn't have a 360 was Beautiful Katamari but I guess I'll tentatively mention Tales of Vesperia here, too. I have it (and vastly prefer it) on PS3 but most people don't have the opportunity to play it since it was never localized, so if the PS3 version didn't exist I would probably still want a 360 just for that game. For PS3, my favourite games are Tales of Graces f and likely the Kingdom Hearts 1.5 HD collection. KH1.5 is remakes from PS2 though so if it doesn't count, so be it. There are many games on PS3 that I have 100+ hours in, though, compared to a very small number of comparative games on 360. Again, I think the only games I played for a decent amount of time on 360 were multi-platform games. As far as exclusives go, I think the PS3 is much more catered to my tastes. I haven't even finished going through all the games I want to try on PS3 that aren't available on 360 whereas the other way around? Yeah, I've played everything I'm interested in on 360 that never made it to PS3. I don't think I'm missing anything great.
