It's a very hard question to me.
I hated this generation of console. Often, when i think about how i'm not satisfied in current gaming, i still think about how bad PS3 vs 360 was. It's actually when i stopped being "mainstream" because i didn't understood the craze with brown shooters. I mean, i started on Macintosh and Windows then thanks to SNES emulators found love with consoles and took a N64 then a Gamecube and a PS2 so i thought i liked any kind of game.
But that generation of console proved me wrong with Call of Duty, Halo, Gears of War, what Resident Evil become to be fair, i was already not a big fan of open world and didn't cared about GTA III so yeah not liking open world like Infamous or Sleeping Dogs didn't helped me ! That's how Prince of Persia became Assassin's Creed which i liked less... Even Uncharted i couldn't like ( especially the first one ) and i found it SO POOR compared to Tomb Raider. I also couldn't understand W-RPG at the time ( so no Oblivion and Mass Effect ) and J RPG were losing their touch at the time ( Err Star Ocean 4, FFXIII, Last Remnant ( sorry Kawazu...) not being understandable, Resonance of Fate being cool at the beginning very repetitive after a while even Tales of Vesperia had a disappointing story...). Even with Nintendo I was disappointed by Mario Galaxy linearity ( the atmosphere was fine but disappeared with the second one ), disappointed in Mario Kart handling, disappointed in Twilight Princess, disappointed in the casual focus...
EVERYTHING wasn't bad at the time of course. It was the revival of fighting game and i loved Blazblue to death; most new CAVE's shmup like Mushihime sama Futari or Deathsmiles were here too even if you couldn't play all of them... Some shooters were interesting enough for me like Bioshock ( even went back to play all the System shock which.. I kinda liked better than Bioshock ah ah ), Portal, Dead Space and Mirror's Edge or everything Platinuum Game made at the time really be it Bayonetta, Vanquish or Madworld ( not Anarchy Reigns... ). But still, it was obvious to me i didn't like ALL video games like i thought before.
So... i mostly played on portable at the time, on DS and PSP with game i really loved like Ace Attorney or Locoroco.... And of course i still played my PS2 at the time, with games like Persona 4 still being out on 2008.
There is still something that gave me hope at the time though... And it was the indie games. I think it's strange to hear today but World of Goo was like, my favorite Wii game at the time. I never thought a video game could also be "a short cool unique experience with a big artistic ambition and a small price". And for that, the Xbox 360 was the best with stuff like the narrative of Braid, the presentation of Limbo, the simplicity of Splosion man, the atmosphere of Scary girl, the joy of Trouble Witch, the fights of Shank, the concept of Fez, the narrator of Bastion and much more... That was my true joy really. Even some Xbox Live Arcade Indie game were fun like the creepy Decay, or the super cheap but very fun Street of Fury
So yeah, Xbox 360 wins right ?
Well.... yeah.... ? But I took a PS3 in 2010 or so and little by little, i found new stuff to like. The time management of Atelier Rorona, the last chapter of Solid Snake life with MGS4, Demon's Soul being that "strange hardcore thing" that i started and completed as Dark Souls began to explode, Tales of Xillia that i liked way better, the reboot of Rayman with Rayman Origins then (arguably later) Legends, 3D Dot Games Heroes or, coming from Trails in the Sky, i was very eager to play Trails of Cold Steel which AT THE TIME at least, i loved ( now i'm more reserved ) and i still loved some Playstation exclusive like Journey or Tokyo Jungle
So i usually say that PS3 was my favorite in the end especially during the Wii U days where i was much more happy in general with gaming. On PS3 i could even play Blazblue online without paying anything ! Now that was SUPER cool, the true democratisation of online for me ! I will always curse Microsoft for making you pay for it, console are the only ones that do that !
But despite this deep grudge, i still think the Xbox 360 brought more to the world in the end... Especially nowadays, when i'm starting to learn how TPS like Gears of War can actually be fun when playing with someone i actually like... And that i found that i find even horrible BTA at the time like Splatterhouse, Dark Sector or XBlades, easily the worst of them all oddly entertaining.
So yeah
TL;DR : Xbox 360 brought more to me thanks to indie games but my grudge for paying online makes me more fond of PS3 in the end.