PS3 in the end. But 360 beat both the PS3 and Wii in the US so, they (MS) certainly have the right to brag.

People often point to how the PS3 sold more units in a year's less time but there is a lot more context to that. 

How much did it cost Sony to achieve that?  Yes, the launch price for the 60gb model was high at $599, but was reduced by $100 with the introduction of the 80gb model at $599, which was also slashed to $499 with a $399 model introduced... all within the first year.  Xbox gained over 3 times the market share it had over the previous generation whereas Playstation lost close to 50% of what PS2 finished at.  And even with the RROD debacle costing Microsoft over $1 billion, Microsoft still finished in the black (largely due to Xbox Live) while Sony lost billions on the PS3.  So I think 360 "won" quite handily.

However, that doesn't mean the Xbox 360 was necessarily better.  While the 360 was widely praised as being more developer friendly (because it was), pretty much every game I cared about still released on the PS3, and in a few years time, most of them were coming out fine (minus a few like Bayonetta, lol).  And there were hardly any exclusives on the 360 that I missed not owning when compared to the Uncharted series, the God of Wars and Metal Gear Solid 4.

Even though Blu-ray at the time really didn't give the games a substantial advantage over their DVD counterparts on 360, I loved that I could watch The Dark Knight and seasons 3 and 4 of LOST in HD on my new BD player when I finally got it at the end of 2008.  The PS3 was also a much more reliable console too from my experience - mine fell off of a table and still works to this day (although it's iffy at loading regular DVDs now), while the RROD failure rate of the earlier 360s was inexcusable.

Finally, the PS3 was a multimedia powerhouse right out of the box as it not only played Blu-rays but supported a lot of file types with the ability to load music and videos onto the HDD itself, customize thumbnails, etc.  These features are wasted on me today but back then it was a boon for me to have it all on a single unit like that.  Also, I liked the UI and XrossMediaBar much better than the blades dashboard that 360 debuted with.

They were both great systems though and I do think the 360 controller was better (mostly due to Sony's garbage d-pad and refusal to stagger the analogue sticks) but in the end I'd say the Xbox 360 was the better games machine for the average person and was a much bigger success for Microsoft and the Xbox brand (although they threw it all away the following generation), but I still preferred the Playstation 3 overall.  Still voted for 360 though.

Definitely the 360. The PS3 is great, but it sold about half of what its predecessor did and was hard to develop games for. It was also expensive. Definitely became better over time, but the 360 just killed it right from the get-go(red ring of death aside)

It's as close to a tie as we've ever had, but I'll give the edge to the 360, mostly because it gained a lot of ground gen over gen whereas the PS3 lost ground.

Technically neither "won" the generation, they finished 2nd/3rd.
The 7th gen though is the only real gen when none of the runner ups really felt like a "loser", all 5 systems did well.

I think I have to more or less put a tie for now.
Most of my gaming on these consoles (especially PS3) have been many years after the console is over.
360 advantages
-Better controller
-Better multiplat performance
-Better online (though it is paid)
PS3 advantages
-Blu-ray
-Sony games
-Free online
-Backwards compatibility (PS2 in early models, so I've never been able to use it)

Xbox 360 won in software units and online subscriptions, and lost billions less than PS3. Other than sheer hardware units or your personal preference, 360 won against PS3. But in gaming history, PS4 and PS5 are in better spots than Xbox One and Xbox Series X/S. Sony built up momentum from the PS3 to PS4, Microsoft lost some from 360 to Xbox One.

Actually, both the PS1 and PS2 both were worse hardware wise then the PS3.  Pretty much all fat PS2 would get DRE issues eventually.  And most the older models of the PS1 would eventually have to be turned upside down in order to work.  They moved the laser locations on later models and the PSOne version to fix that problem.

More than 60 % of the fat PS3 models would get YLOD eventually, and that's much more difficult to fix than a faulty laser or disc drive.

Agreed.  Only generation where multiple of my consoles died.  Had RRoD and YLoD...  absurd.  

The most convincing assessment of the situation is that almost every game from the inception of the Xbox 360, when it was also released on PS3, looked and ran better.
The selection of exclusive games gave the PS3 a slight advantage. Nothing else to describe that generation. Very unique and well the same for every console.