Yeah, when Don Mattrick took over after Peter Moore left Microsoft in like '08 IIRC? Then Don really started changing everything that Xbox was about in that early 360 era. 

One of my biggest "what if's?" in Xbox history is what if Peter Moore stayed on at least until the launch of the Xbox One? It most likely wouldn't have even been called the Xbox One because the "One" in the name was about the system being an All-In-One entertainment system. Something that Don Mattrick explicitly championed, along with the Kinect. 

Shame we had less than a decade of Xbox actually being an objectively good ecosystem. At least in the traditional sense. 

Without question the 360. However. And this is a big however. I believe that 50% of 360's died to RROD and this bumped sales significantly making the console appear more popular than it was, I can't find it now but I used to have solid evidence that the failure rate was slightly above 50%. I lost one, everyone I knew who had the original model lost at least one and one fool I knew bought the console four times (used 3 times) after me trying to get it into his skull to just buy an elite model after the second failure which I believe didn't have the same failure rate. So, I believe Xbox has stayed as popular as they have ever been up until this generation where they seem to be slipping off. I don't believe there ever was a point where Xbox was winning the 7th gen apart fron the first two years where they had the early start and Sony stunned release in regions. I belive PS3 caught right up to them much sooner than the numbers implied.

Found on some scource not sure if it's right ai haven'tchecked into it:

54.2%
Microsoft's Xbox 360 has an overall first-time hardware failure rate of 54.2% among its readers, according to a report by print magazine Game Informer in its latest issue -- and 41.2% of those users were said to have multiple failures.

I agree that the main reason behind the initial margin between X360 and PS3 was the one year gap. And X360 used these months to buy some timed exclusive games in 2006-2007 like Lost Planet or Portal. While development of some games for PS3 was more difficult, it wasn't the main factor of delays. Many of these games were released one year after launch on X360. It's obvious that there were exclusive deals. But then in 2008 a lot of games were launched on both consoles on day one. (even if some games performed better on X360) There was a marketing deal between Take-Two and Xbox about Grand Theft Auto 4 but then the game launched on both consoles on day one, even earlier than on PC.

Also PS3 always sold better in Asian countries. Japan market is obvious example although MS tried to improve sales there in 2005-2007. In the first two years MS released some exclusive japanese titles but it didn't work. The situation in asian countries hasn't improved since those times.

Finally, it took 7 years for PS3 to reach the number which X360 reached in 8 year period of time. By the end of 2013 they have had the same number of units sold. 

By far the Xbox 360. Even just taking into account the 2005-2010 part of its life, it still blows out any other Xbox console for me...The last 2 years or so were pretty mediocre to be sure.  It had some amazing JRPGs that were exclusive at the time, CoD+BF were peak (and just played/felt better on the 360 IMO), Xbox's first party was pumping out good games, etc....

Just about the only notable problem from 2005-2010 (and it was a big one) was the RROD. It wasn't really fully fixed in the manufacturing process until about 2008, meaning for about half of the market availability (over 2 years) of the OG Xbox 360 SKUs had a far higher failure rate than they should've. 

I mean paid online, even for free games, was always a problem for 360 to this day but RROD is worse. 

If you didn't like Kinect, first and third-party exclusives more or less died after 2010 with some exceptions like Gears 3 and Halo 4. But compared to what was pumped out from 2005-2010, not even close. 

Xbox 360 and Wii were front and middle-heavy in terms of software players liked. PS3 was middle and late-heavy. Stuff like Uncharted 3 and The Last of Us (heck even Journey in 2013) was putting most of Microsoft and Nintendo's first-party offerings to shame in 2011-2013. Not to mention a third-party Sony timed exclusive like Persona 5 that was better on PS4 and sold far more on it but was such an amazing game to release so late on PS3 after it was replaced. 

I actually disagree with the notion that 360's last few years were weak.

2011-2015 saw the likes Gears of War 3, Gears of War Judgement, Halo 4, Witcher 2, Forza 4, Forza Horizon 1 & 2, Rise of the Tomb Raider, Titanfall, plus it still got almost every big multiplat game including Skyrim, Bioshock Infinite, Arkham City, Portal 2, Dishonoured, GTA5, etc.

It's last few wasn't as strong as its first 5, sure, but I as a 360 owner I still had tons of great stuff to play.

I never had an Xbox, but from what I see, I think Xbox 360 is probably the best.

It had an insane library, some of the most praised games from that generation, and it managed to fight neck-to-neck with the PS3, even outselling it in some territories.

I gotta go with the 360; tons of killer games and the superior version of most multiplats.

The original Xbox was cool too, I actually liked it more than the Gamecube and PS2 thanks to stuff like Halo 1/2, Panzer Dragoon Orta, Jade Empire, Doom 3, Crimson Skies, etc.

Never owned an Xbone as it never got enough exclusives to interest me, but I played a lot of its third party titles on Switch and PS5. It had some great multiplatform games, but its first party lineup never appealed to me.

Was planning to get an Xbox Series, but now that their games are coming to PS5 there's no point.

Ouch. Xbox One doesn't even have one vote. I think that's for a few reasons
-The underpowered Xbox One. Yeah, it was a generational leap over the Xbox 360. But the 360 was way more comparable to Gaming PCs in 2005 than the One was to Gaming PCs in 2013 (same dynamic with PS3 in 2006 and PS4 in 2013). Xbox One X fixed this, but it's not the base console and was sold as a premium offering.
-Xbox Series X/S are very similar to Xbox One but with SSDs, better specs (namely Xbox One vs. Series X) and a larger game library. It's only some Kinect 2.0 Xbox One games that aren't compatible with Xbox Series.

OG. It's the one that really had its own identity. All Xboxes after that were just too similar to the PlayStation, just with slightly different libraries and capabilities. But the original was considerably more powerful than the GC and PS2. And it actually has a respectable list of exclusives including Fable, Sudeki, KOTOR, Ninja Gaiden, Jade Empire, Shenmue 2, Morrowind, Doom 3, etc. And it usually had the best version multiplats.