Simple.
Without taking into account the 8th gen, ask yourself which company would you rather have been. Looking at it from a business point of view and not as a fan, you'd have to say M$. Unless it's been my debunked, the PS3 was said to be a big money loser for Sony whilst the Xbox 360 supposedly made some money--just not the kind of money that Microsoft wanted it to make.

This is based on forum posts. I'm sure concrete numbers are out there. I just don't know where to look. Plus I'm lazy.

It was a pyrrhic victory for Sony in my book. They just barely managed to outsell the 360, but it cost them way too much. On the other hand they laid the groundwork for the success of the PS4 back in the day while MS just completely lost it at the end of the gen and burned everything they built up over years in a matter of days.

It sure was a fun time to be a gamer though.

Depends on what metric you want to use.

Market share?  Basically a tie.  Sony slightly ahead on hardware and Microsoft slightly ahead on software.  Basically a tie.

Profits?  They both lost a ton over the course of the generation.  (While Nintendo made record profits.)  Again basically a tie. 

Which one accomplished their goals?  This is the most interesting metric.  Sony had several goals for the PS3:
1) Continue the success of the PS2.
2) Make Blu-Ray the dominant disc format.
3) Develop the PS3 with PC-like capabilities effectively putting a Sony PC in every gamer's living room.

In contrast, Microsoft only had one goal: Stop Sony from accomplishing their #3 goal, which is a threat to Microsoft's core business.

How did they do?  Sony accomplished their #2 goal.  They didn't accomplish #1 and #3.  Microsoft, on the other hand accomplished their only real goal.  PS3 started out with a lot of features that Sony eventually removed.  Among these were having 4 USB ports and being Red Hat Linux capable.  (PS3 also had other PC-like features that didn't get removed like an internet browser.)  The USB ports soon got scaled down to 2 and Sony removed their Linux capability.  The latter feature is really the big one, because you can't really have a PC without an OS.  (Also they pissed some hackers off by doing this and Sony's system got hacked.)

In the end, I have to give it to Microsoft.  They accomplished their only one goal.  Sony, on the other hand went into Generation 7 overconfident and they got seriously humbled.  Among the 2 losers of Generation 7, Microsoft is the winner.

Wii had a lot of great games... yeah, but only a fraction of great PS3 + Xbox360 games:

• Wii had 14 games with a MetaScore of 90+, PS3 + Xbox360 each had over 50 of them.
• Wii had 43 games with a MetaScore of 85+, PS3 + Xbox360 each had around 180 of them.
• Wii had 106 games with a MetaScore of 80+, PS3 + Xbox360 each had over 400 of them.

https://www.metacritic.com/browse/games/score/metascore/all/wii/all?sort=desc&page=0

I think the most important question is; who cares?

Yeah the numbers look like a tie between the PS3 and Xbox 360.  However, I'll give PS3 and Sony the edge for climbing out of a huge hole at the outset and catching the 360 in sales and the "cool" factor having spotted the 360 an entire year of production.  Pretty amazing feat...

Sony made the right decisions after that first year, and in the end made the PS3 a great product based on price, features and most of all, great games.

Seriously, those last PS3 games were fabulous especially the Last of Us-- fully using the hardware potential of the Cell Processor.

Maybe the best decision the Sony leadership made was to hire Mark Cerny to immediately work on the the next PS4 console which made up for the failed launch of the PS3 and became the go-to console for gamers.  I've always thought between the Sony PS4 and a moderate gaming PC, you are pretty much covered unless you also want the Nintendo Switch games.

So at the point the generation ended, Sony were in a great position but MS were quite weak.  This transferred over to the current generation.

I'd say this is the reason why Sony won the generation out of those two.  

Microsoft won because they took over the two most important regions in the console gaming space NA and UK. Not to mention thanks to the 360 generation Microsoft is now relevant and if rumours are true about the cheaper xbox one series s, I think they will take over NA and UK again.

Also, it seems PS3 lost all of the money Sony made on PS2 and PS1.

360 sold more software. Ps3 edged out on hardware. Overall I’d call 360 a western dominated console while PS3 dominated in the East. Since I live in the west I’m happy with how it turned out.
Take away Japan and Ps3 loses its crutch that Xbox has to make due without. For the majority of us, we lived in Xbox country :)

Overall it was a strategic victory. Xbox tripled their hardware sales gen over gen while Sony’s was cut. That’s right, might be a DJ part-time. Because I know how to spin 

Financially both didn't meet thier expectations.
Commercially PS went from a 75% market share to 30%, form selling 5 times more units than XB to 1:1.
The XB went from 12% marketshare to 30%, and increased hardware sales by 4 times.
Commercially I think the winner is clear.
In fact the X360 effect on brand recognition and loyalty was so strong it allowed MS to stay relevant in the console space even thought they got everything wrong in the following generation.