But how many of those Xbox sales where due to RROD failures?

I'd say Microsoft was the short-term winner of that war, but Sony was the long-term winner. Microsoft came out of the generation better financially and also made enough money from the Kinect to offset their losses from the RRoD mess. However, the Kinect ended up sending down completely the wrong path for the Xbox One, and they have yet to recover from it.

PS3 could definitely have gone a lot better, but Sony shored up their first-party development in response to third-party developers tending to half-ass their ports for the system, and the PS3's having a Blu-Ray drive helped completely destroy HD-DVD in short order, both of which really paid off in the longer run.

I remember when GTA 5 came out, the ps3 quickly became the console to get. The game was on 360 but everyone I knew talked about it as a ps3 game. Before then it wasn't really relevant. Now of course the sales leave them asbasically equal on paper but I do wonder which will be remembered more fondly?
Also which console and it's software was more profitable?
It's all perspective I guess.

If we just counting that generation, the 360 won with xbox live, profits, and greater gain compared to last gen. The 360 continued off the great things from OG Xbox and introduced a few more with an early launch to boot.

If we count the big picture, I think the PS3 won because the late surge and commitment to constant first party support as well as free online helped consumer trust with the PS brand. The PS4 built off that consumer trust and introduced online fees to rake in a ton of profit. The PS3 failure made Sony become more dev friendly and consumer friendly.

There’s a flip side to that argument. People rebuying a faulty console instead of a fully functioning PS3 speaks to the strength of the 360 brand 

I've been seeing that argument since like '07 but I don't know. Microsoft repaired mine for free. They kept that policy for two years after purchase (cost them like a billion dollars, if I recall). After that, I bought more 360 consoles because I wanted to and not because I had to. I'm pretty sure repairs don't count in the overall total.

Hard to say.  I know people who sent their 360's back to Microsoft and had them fixed.  Others like me and my brother got temporary fixes at local game shops, and then upgraded to the Slim that had built in wifi and was just flat out better than the original 360.  So, that's more like separating same customer sales by hardware revision.  How many in PS4's sold # are same customer sales between PS4 and PS4Pro, or Xbox One and Xbox One X.  It's admittedly not the same situation, but same customer sales have muddied the water of actual hardware sold for a long time now.  How many more Wii's would have sold later in the gen if Nintendo had released an actual branded HD Wii instead of going straight into the Wii U with Gamepad?

To OP, I would say that if you look at the small picture, then Microsoft won that round.  But if you look at the big picture, then Sony won.

I know, I just say that to those who are convinced people scrapped their 360 and bought a new one. 

No...  if we use that logic, where we judge who won a generation by the sales of the next one, then the PS2 and XBox essentially tied, and the Wii, DS, and PSP were all horrible failures.

Did the kid who got a 95m head start on the 100m dash win when it crossed the finish line at the same time as the pro athletes?