Which system was best for you between the two? Who really won that generation between the HD twins ? If you could take only one with you (with the full original library or even the full library on a modded console) which would it be, and why? Reminding you here that PS3 had model with full back compat for PS1 and PS2, while the 360 had also compatibility with OG Xbox games (which were better than PS2 versions). Both of them had also emulators when modded. You can take into account the total sales for each system if you want, the games, the longevity, the legacy they leave after, or the system themselves alongside all the models/revisions. I will add some sales data (launch aligned) here:

While the sales ended up close, the 360 definitly jumped out of the gate. I remember having around 80 /10 games split in favour of the 360 after the first few years but ended up with around a hundred 360 games and double that for PS3, so the momentum that was with Sony/PS4 at the end of the gen was why I gave it to the PS3 .

Started out with Xbox ahead. But PS3 ended up gaining the momentum that propelled the PS4 ahead and kept PlayStation in front of Xbox. If 360 had won, we’d be in a very different console landscape today. For better or for worse.

They're two of my favourite consoles of all time, but they both lost a fuckton of money early on (not sure if PS3 ever actually recouped its losses actually) and finished well behind the market leader at the end of the day.

Of the two, I liked the 360 more due to the more comfortable controller, stronger library, and superior performance in most multiplats.

360 is my fave console of that generation even if it is missing EX Troopers and some Japanese mech games like ACE and some Gundam Stuff. I still find that 360 and the controller a much better experience. I detest PS3's install times. Interface and controller. PS3 is only tolerable to use with a 3rd party controller I use. Also nice that a lot of games that gen just run better on Xbox 360. I will take Gears of War over any Sony PS3 first party game even tho I liked Lost in Rain & Folklore.

Both? 360 started stronger, but PS3 finished much better. In the end, both were decently successful and had great libraries.

The best for me PS3.
The gen winner Xbox 360.

The 360 definitely took the outer bailey, but PS3 managed to hold the keep in the end.

Seriously, when it comes to hardware the 7th generation was one of the worst imo, The Xbox 360 and PS3 were both the most unreliable systems their respective companies have released. I am also not a fan of either controller, a shitty d-pad is a deal breaker for me, and 360 has one of the worst, even if the controller is otherwise really solid. The DualShock 3 was stock in the past with the PS1 design, but the buttons somehow felt even worse and the triggers were particularly poor. The game library across those two systems was strong, which I guess is the big saving grace, but I would rather find another way to play those games.
I think it also cannot be understated how poorly some of those PS3 ports run, it often entered broken territory, Bayonetta, Skyrim, Fallout, Shadow of Mordor, F.E.A.R, The Orange Box. etc.

So if I had to take one of these with me, it would have to be one of the later models of either, even if PS3 ditched PS2 compatibility. PS3 still has some interesting games that aren't playable elsewhere, which is a major plus, and overall it's first party stuff is just stronger. Still I would probably go with an Xbox 360 S or E, as it at least had some solid versions of the most important games of that era.