Depends on who you ask. 360 has some popularity here, most certainly, but nothing on the level of Sony. Nintendo always has a core group and they're looking to overlap that at this time.
However, Sony's making huge mistakes this round and I don't feel they'll be capable of continuing domination. This is Nintendo all over again from the 90s. Consumers yelling, developers hollaring.. Sony's going to have to learn the same lesson Nintendo did. And while Sony is a mega-corp, if their gaming division goes under it's most definitely bad for Sony Corp as a whole. Their stock is in such terrible shape right now, they couldn't handle a faulty Ps3 "launch"/first year.
The scenario as I see it:
Sony fails to sell through a significant portion in Japan as seen by developers.
Developers jump ship to the system with more userbase (this is the DS/Wii).
Dragon Quest IX goes to Wii.
Every Japanese gamer goes to Wii.
Western gamers are heavily affected by this, despite what many here will tell you.
HOWEVER. If you liked your X Box, and you like your 360, keep on liking it. It's like Nintendo's core audience - they're going to cater to you and you're going to love it. In my case? For about twenty years now I've been a Nintendo fan. That's never going to change. There have been other games that have come along and stolen my heart (Xenogears, Devil May Cry, Sonic the Hedgehog, etc), but I'll never forget Mario Bros and that first time. I still play Mario Bros. weekly.