So it had nothing to do with the fact that the PS2 sold over 140m and the Xbox barely 30m? 5 PS2's failing would be 1 Xbox failing...

That really depends.  At one point the PS3's failure rate was 40%.  Granted, that was only in Europe and only applied to a batch of consoles, but in a given space and time the PS3's failure rate was an high as 40%.  It's still consistently 10%, where as the Xbox 360's failure rate is lower. 

The Xbox 360's high failure rate is attributed to those Xbox 360s that had the Xenon/Zephyr boards sold through 2007.  After that, the failure rate steadily fell.  With the Jasper boards, that failure rate fell to about 1%.

The Durango processor has a massive heat sink and a massive fan.  My guess is that Microsoft made sure this go-around that not only was the device going to run as cool as possible, but any failures were going to be heavily investigated to ensure they were/are resolved before manufacturing.  Engineers weren't oblivious to the Xbox 360's problem, they just believed it would work itself out as manufacturing improved.  That was a misunderstanding of the problem.  I get the feeling they are more willing to aggressively pursue any issues now rather than have to deal with problems later so as to not repeat the debacle of the RRoD.

You seem to have an understanding of what really happened and the values for the respective failures, so I won't doubt you, but where did you get the info from? I know I read somewhere that the old 360s where way higher than the PS3. I think I read somewhere that the PS3's failure rate was about 4%, but I can't remember where. All sources seem to specify very different values, though.

But I do remember that the 360's failure rate decreased significantly when they changed the boards.

The PS3's failure rate has never been 40%. You can't take one batch and say it applies to the whole console. That is like saying "at one point the 360's failure rate was 100%" because in the given space of "my house" the 360 broke.

And the 360 has never had a lower failure rate than the PS3. Have you seen this? http://www.polygon.com/2013/5/25/4365392/microsoft-shooting-to-sell-25-million-more-xbox-360-units That is Microsoft saying they expect to get another 12.5 million sales from replacements. That means if they think every single person whose 360 breaks buys a new one, the 360 has a failure rate of 16% (and I doubt they think that everyone buys a replacement).

There was a published article regarding the nature of the Xbox 360's failure around the time that Microsoft acknowledged the problem.

To my knowledge, there hasn't been a more recent analysis than the one Square Trade did.  However, based on their analysis, Jasper-based Xbox 360's, which the Xbox 360 S would be similar to, dropped to 1%.

Well, Germany is a large area.  So when a retailer in Germany says, 40% of our PS3 sales were returned due to DOA sales, that's not the same as it's 100% in your home. 

You do realize there are people who buy consoles based solely on the latest and greatest.  They don't buy a single console and keep it until it breaks, they buy repeatedly new variations or features.  If the next model integrates with the Xbox One to provide backward compatibility, I'll certainly be buying a replacement Xbox 360.  So what?  So what if Microsoft is estimating that 12.5m Xbox 360 owners value backward compatibility and want a solution that integrates with the latest and greatest technology?  I don't, however, doubt that there will be Xbox 360 failures, but I highly doubt given the low rate of failure of the Xbox 360 S, that they're counting on 12.5m consoles being replaced because of console failures.

Did you mean dropped to 1% above PS3?

http://www.squaretrade.com/htm/pdf/SquareTrade_Xbox360_PS3_Wii_Reliability_0809.pdf

It is pretty interesting. The PS3 is worst for disc read errors (probably due to bluray being new) and the Wii is worst for power (don't know why) and control issues (more obvious).

It's interesting to note (judging from that document) that without the RROD the failure rates are almost the same between PS3 and 360.

I'm just curious to know where in the graphs present in that document they included the PS3 YLOD or if they bothered to include it at all.