I think going with regular DVDs was a smart move by Microsoft. Both Bluray and HD-DVD were new formats by the time the Xbox 360 was released in 2005 and would have driven the cost up massively. At that time, SD TVs were still the norm, HD content wasnt widely adopted yet. By going with DVDs over Bluray or HD-DVD Microsoft was able to keep the cost down. Remember, the premium model of the Xbox 360 was $399 at launch, the PS3 was launched a whole year later for $599. That's a huge price difference.
While the PS3 was certainly well priced package (it was one of the cheapest bluray players available and could also play games), for the gamer the experience on screen was practically identical between the two systems, even with the upcoming rise of HD screens.
Yet, the PS3 experience was 50% more expensive due to the technology which I believe gave Microsoft the edge. Their system was considerably cheaper, and the user experience was the same.
After all, the multi disc games took years to arrive and weren't common, either I do have a considerable and only a handful of titles come with two discs, some of which are even just optional (both forza 3 and 4 came on two discs containing a number of cars, but you could play the game without this content.)
By the time HD content was adopted by the consumer, standalone bluray players were available for cheap. Sony was not able to repeat the strategy of the PS2 with the PS3.