360 had a better start.
Ps3 ended great, but after a lot of years with poor ports, almost zero exclusives and worse online framework.
From 2005 to 2010 XboX had Perfect Dark Zero, Quake IV, DoA 4, Divinity 2, Condemned : Criminal Origins, Dead Rising, Bioshock, Mass Effect, Blue Dragon, Lost Odyssey, Gears of War 1 and 2, Halo 3, a lot of exclusive Live Games, Metro 2033, Spider-Man Friend or Foe, Velvet Assassin, Alan Wake, Virtua Fighter 5, Halo Reach, Left 4 Dead 1 and 2, The Witcher 2, Forza Motorsport 3, etc
In addition, a lot of Sony exclusives were made multiplatform : Tekken, Final Fantasy 13 and spin offs, WWE games, etc.
Not all of them were masterpieces (Velvet Assassin, Perfect Dark Zero, Quake IV) other ones were ported for Ps3 later on (Alone in the Dark, Mass Effect and Dead Rising 1), but Xbox 360 had objectively better and more games at the beginning of the generation and even the bad games (Too Human) had a lot of hype around them and sold very well, generally.
In the same time span Ps3 just had God of War 3, an enhanced version of Alone in the Dark, Gran Turismo, Siren Blood Curse and of course MGS 4.
Too little too few.
Of course I may have forgotten a couple of titles, others I wasn't interested in, but in 2007 I had to buy a console, I just picked the one I felt more connected with.
From 2010 to 2013 of course Ps3 regained a lot of lost ground with the Infamous series, Uncharted Trilogy (although the first one wasn't that impressive) and the Last of Us, which unfortunately was just the Swan song of Ps3.
I want to clarify, in order to avoid any console war, that I always was and still be mainly a PS user, having a PS one, PS2, PS Vita and Ps4. So 360 was the only Non-Sony console I ever owned.
The reason why I picked ps4 over Xbox One this generation is the same as above : too little too few in terms of single player, immersive Sim exclusive games.