Compared to the original XB, it did. I was not referring just to absolute numbers strong, but growth, expectation, hype (gears of war in 2006 and every new exclusive game that were announced during E3 at 2005 and 2006 like Bioshock, Mass Effect, Halo 3, GTA IV simultanous release ....) were an indication that X360 was going up hard, and soon and that PS was going to have real competion in USA for the first time. And that was what happened. For PS3 at launch, exclusives were lost and the ones PS3 had were compared to X360 ones, and PS3 had worse ones. Microsoft had Halo and Gears of War and Sony had nothing to compete against that.
Edit: To put a personal example, that Gears of War ad in 2006 almost made me buy an X360 by then. Me, a spanish person, who loved Playstation since PS1 era and knew nothing about XB.
Xbox NPD end of 2002-4.6 million
Xbox shipments end of 2002-8.0 million
360 NPD end of 2006-4.5 million
360 sell through end of 2006-8.0 million
360 was about even in the US and a bit higher everywhere else.
Sure, E3 2005/2006 had some big stuff for 360 but so did E3 2001/2002 for Xbox. Halo, Xbox Live, Knights of the Old Republic, Splinter Cell, Ninja Gaiden, Halo 2 tease, etc.
360 did not start out fast, that is nothing more than revisionist history. It was actually mocked as being Xbox 1.5 initially because it seemed like such a small jump over Xbox.
I repeat. I wasn't talking just about the sales (so i'm not saying X360 sold faster than XB in its first year, i never said that). I was talking about the perception of X360 when PS3 launched. XB brand was in a much better position during 2006 than during PS2/XB era. By 2005 XB Live, Halo 2, X360 launch were something more popular in USA than anything before for Microsoft. In fact, the exponential growth in popularity and sales for XB during 2004 to 2010 was spectacular, and it started around 2006 thanks to X360.
So again, XB brand has never been in a better upward trayectory than in those years (before or after). After a year X360 launched, the sky was the limit back then and I still consider it the golden years for XB (2004-2008).
People wanted new things for the next gen, and there was nothing more popular for the american audience during those years than playing online with XB Live with Halo 2 and then games like Gears of War and Halo 3 were king in USA. Halo 3 hype was way bigger than any hype the original Halo had for the original XB, it wasn't close. That affected a lot PS3 sales in USA in 2007 and for the rest of the gen. X360 had better exclusives and better services than PS3 at a better price during 2006-2007. It's not revisionist history, it's an explanation as to why XB went from selling almost 15M lifetime from 2001-2005 and lag behind way far to PS2 in US to sell almost the same in half the time and becoming the best selling console of the gen in US in the end. It was thanks to that good start. Without it, X360 would never had sold as much as it did (and i know Kinect helped a lot in 2010 afterwards, but without X360 success during 2006-2009, Kinect would had never been a success in the first place).
In the end, X360 convinced people to buy a Microsoft console unlike XB and XBO did against PS2 and PS4, and that's my point.