Nope. The Xbox 360 launched in November of 2005. The PlayStation 3 launched in November of 2006.
The PS3 started outselling the Xbox 360 for the year in 2007 and kept steadily gaining on the Xbox in total sales for the generation until it overtook it.
Xbox's one year head start kept it level with the PlayStation 3 for quite a while but it lost out in the end.
Look at the global yearly sales figures on VGChartz. From 2007 the PS3 outsold the Xbox 360 every year except for 2008:
I think a lot of people bought the PS3 as a bluray player.
The charts you link to show game sales that lag way behind the xbox. For example Skyrim sold 2.6 million in 2011 on the xbox and only a million on the ps3.
I only say this because I got my ps3 for free with the purchase of a Sony television at a Sony store (remember those?) in late 2009 and never purchased more than a bare handful of games which I almost never played.
After the cost-reduced redesign in 2009 Sony gave away a free ps3 with every television purchase in Sony stores for almost an entire year.
Skyrim was one the games I bought and it was so buggy, even for Bethesda, on the ps3 due to ram limitations (I've read) that I purchased it again for pc.
Used my ps3 to watch a ton of blurays and Netflix, though. My ps3 was, and based on those yearly charts a lot of other peoples' ps3s were also, extremely powerful streaming boxes and I only retired mine when I upgraded to a 4k tv and got an appletv 4k.
> For example Skyrim sold 2.6 million in 2011 on the xbox and only a million on the ps3.
You have to consider total software sales, not individual titles. And for the PS3 you have to consider its impact on blu-ray movie sales (which aren't in those charts).
Blu-ray also launched in 2006 and the PS3 was one of the most useful players available because it could do more than just play movies.
"The charts you link to show game sales that lag way behind the xbox. For example Skyrim sold 2.6 million in 2011 on the xbox and only a million on the ps3."
As you write later, Skyrim sucked on PS3 (like other multiplatform games like Bayonetta). It is not strange that it sold much less since it was a much worser game on the PS3.
The PS3 started outselling the Xbox 360 for the year in 2007 and kept steadily gaining on the Xbox in total sales for the generation until it overtook it.
Xbox's one year head start kept it level with the PlayStation 3 for quite a while but it lost out in the end.
Look at the global yearly sales figures on VGChartz. From 2007 the PS3 outsold the Xbox 360 every year except for 2008:
https://www.vgchartz.com/yearly/