Saying it's "brand loyalty" is a bit of a shallow analysis. Quin's already pointed out that even with RROD taken into account, for a very long time a 360 was a hell of a lot cheaper than a PS3. Beyond that though, Microsoft knew they weren't going to win big with the original Xbox in terms of sales and they always intended to use it to build up a solid core of customers and franchises to attract people for their second console. The original Xbox was a surprisingly great console with a terrific lineup and games like Halo put the thing on the map; a decade later that particular franchise is a household name comparable to Mario and Pokemon.

When the Seventh gen came along, Sony lost the plot. They put out a tremendously expensive console that was missing perhaps the most important possible feature, backwards compatibility, in all but one SKU. Their lineup wasn't tremendously impressive but more to the point Microsoft did a damned good job of showing and telling people about their features, whilst Sony pretty much assumed they could coast along. If it had had a sane price point they almost certainly could have but the absurd cost of the PS3 meant people turned elsewhere. Their list of exclusives was frankly underwhelming and those which did exist were subject to tremendous delays. Gran Turismo 5 is probably the best example there.

It seems to me that the crazier brand loyalty is to the system which took forever to arrive, was extortionately expensive, lacked videogames, and was pretty underwhelming in most regards. If people stuck with the 360 despite the RRoD debacle there might be a reason for that beyond people who think Microsoft are really great and Bill Gates looks like such a nice man in his nerd sweaters.