Of the launch models and up until summer of 2008. After summer 2008 they made them tanks. There is little to no YLOD FAT consoles produced after summer 2008. Much like the 360, where they get it very reliable with jaspers and tonaskets (late 2008 through summer 2010) the same happened with the latest FAT revisions on the PS3.

Sure, the later models are much much more reliable. But we are talking 2-3 years before they even launched. And if you want that backwards compatible PS3 model, you have to deal with the unreliable model.
Edit - It was also only SOME of the 2008-2009 revised fat PS3 models that were more reliable. 

There was no easy fix for the fat PS2's that would get DRE issues.  Most people that had one just bought a new model or if they were smart, they bought a new one put the faulty unit in the box of the new one and returned it to the store and asked for a refund.  As for the faulty original PS1 even if you fixed the laser it would go bad again eventually since it was designed wrong and the laser was too close to the power supply.  

A lot of PS2 DRE issues can literally be fixed with simply cleaning the laser properly. Replacing the laser is also not that difficult.

I know the original PS1 was particularly shitty in that regard, and you might have to go through a lot of lasers. Still, much preferable to most YLOD issues. You can also just mod the PS2 or PS1 to boot the game from a memory card or USB.

You are probably pointing to the CECHQxx and CECHMxx, but those were produced in very limited quantities and only for Japan and UK respectively. They were produced only for the bundles with " Final Fantasy 7 " and " 300 " the movie, respectively. So it's pretty much irrelevant to include those as argument. Almost all of the sold units after the summer 2008 were the better revisions with 65/65nm chips. " Some " means like 20-30% out of all, where in reality it's close to 100% out of all were revised models - 65/65nm. Other than that, yes, the backward compat models were unreliable and very noisy.

As far as games goes, IMO, PS3 won.

As far as money goes, 360 was making rounds around PS3, gaining insane marketshare in the early years and actually making some money out of it, while Sony was losing so much money.

But even so, from midway until the end of the generation everything was about the PS3 and it really lead for the success of the PS4 start, we all know XBO own mistakes made it a lot easier for Sony, but by the time The Last of Us released it was really as if the 360 did even exist anymore, everything was about Sony again.

IMO, PS3 won, even as the 360 was way better for MS than the PS3 was for Sony, when the generation finished it was very clearly with Sony comfortably on top as far as I could tell from online presence.

Fair! Didn't know those models were so rare.

I remember having to choose between one or the other back in the day. Videogames in my country are expensive, more than the usual compare to the rest of the world so, i had to make a choice. I usually buy consoles after the sucessor hit the market, so the ps4 and xbone were already out (barely though). I already had a Nintendo Wii and a 3DS.
It all comes down to exclusives. The PS3 had a selection of games more keen to my taste, so i went with that. Also, Persona 5 was right around the corner too and i was a big fan of Persona 3 and 4 back in the ps2 days. It was a no brainer for me at the time.

As crazy as it might sound, I've never actually played a PS3 nor XB360 game unless you count the PS5 remake of TLoU:Pt1 or Portal 1 on Nintendo Switch. That said... I do not believe I am informed enough to give any sort of answer here as far as "Which was the better console in the end?" is concerned.
As far as commerical success is concerned: Definitely Xbox. While yes the PS3 did win in the end when it came to overall hardware sales, this victory was accompanied by some hefty annual loses. Xbox was in strong relations with third-party, and managed to pretty much match PS3 in the end despite having virtually no presence in JP, all while maintaining a non-red annual income stream.