I was a PS2 owner from late 2001 through the present. I did not buy and original X-Box until a friend of mine thought he broke his and gave it to me for free (after hiding it and buying a new one he did not want to tell his wife about)...
I did not buy a 360 at launch. I was curious, but I did not see it as ultra-compelling to wait in line for or to pay ridiculous E-Bay mark-ups for in the Holiday 2005 period. I finally bought one when I found it in March of 2006.
From March of 2006 through the March 2007, my XB360 received 100% of my gaming time. It completely replaced my XB1 and PS2 in very short order...I was hooked on LIVE in a matter of weeks (after initially being VERY skeptical about PAYING for online services that were free on the PS2)...
I bought a PS3 in late-December of 2006. It was not exactly a launch unit, but it was part of the second shipment available in my area. I had been jazzed about getting one since I had first seen the Killzone 2 CGI trailer years earlier.
From January 2007 through January 2008 I believe my PS3 received MAYBE 10% of my gaming time....most disturbing of all was the fact that I used my $600 PS2 emulator to play PS2 games more frequently than I used it to play actual PS3 games, and in EVERY case I chose to purchase a 360 version of a multi-platform title over the PS3 version.
3rd party titles (for whatever reasons) were simply better or more compelling to own and play on the 360 platform and LIVE. System exclusives like Resistance (nice, but not really 'better' than BF2:MC or Far Cry:Instincts - which I liked both but many people did not like either one; GRAW 1 or 2, Halo 3 or COD2/3/or 4 as far as ), Heavenly Sword (total let down because I have played more God of War 1 and 2 on my PS3 than I have played Heavenly Sword) and Motorstorm all fell pretty flat with me.
The only game that I played on my PS3 that was a really great game (IMO) was Uncharted....and even at that, in reality it was a spruced up version of Tomb Raider : Legend with new characters...
Why bother with any of this information?
Merely to point out that the XB360 changed my mind about Microsoft and their role in gaming in the future. I was NOT a big XB1 fan....I eventually got one and did enjoy it to an extent, but only as a distant supplement to my PS2. For me, the 360 has currently assumed the role my PS2 used to enjoy and my PS3 has been relegated to the role of HD-movie player and secondary gaming system.
Maybe Sony's games will do enough to change that, but realistically, I do not see a generational difference between XB360 and PS3 games - unless MS stays with the no required HDD ever stance. Last time around I was a PS2 guy through and through and accepted that even if the XB1 had SLIGHTLY better graphics on some games, that what I had on the PS2 was pretty close and at worst was acceptable.
Microsoft set out to do exactly this - convert some of the market to their product and cut into the PS2's dominance...in that regard, the 360 must be considered a success. In the longer term, life of a console sense, I don't think anyone is going to really be surprised in 2009 when the specs for the next XB are released just as Sony is trumpetting the success of the PS3 overtaking the 360 in total console sales.
If a goal for MS was to bleed Sony on the PS3 and decrease their position of total dominance in the games market, then again they have been highly successful with the 360. They are a smashing success in the NA and GB markets and not so much in EU and abysmal in the Xenophobic Japanese market.
But all of that aside, the only really consistently stated goal for MS was to convert their Games and Entertainment Division for a loss-leader to a profitable division in the lifespan of the 360. Well, MS reported the division in the black already (quarterly anyway) and that makes the 360 a complete success and virtually guarantees a MS presence for at least one more generation of hardware around December 2010 or 2011.