It's redefined each generation. This generation is about motion controls as the top seller of all time, the Nintendo DS, has motion controls alongside its console brother the Wii which also does. Sure the 360 has stream lined the online experience, however it has also introduced gamers to the closed era of consoles. You want a bigger HD? Sure just pay an absolute premium on it. Not to mention the 360's hardware problems which have been conveniently forgotten.
The fact that you're comparing the Wii to flash games is absurd. It's fine not to like the Wii, I know I don't like it besides some drunken debauchery, but its impact on the industry is clear. Clear enough that Microsoft and Sony are both coming out with motion control products in the next year.
And for the hardcore gamers I know, XBox Live is a redefinition of consoles. Before Live, PCs were the only serious online game in town, now the XBox actually offers a better (less painful) online experience. Sony's online system is a joke in comparison.
(I own none of these systems, but I'm an ex-gamer and know a lot of gamers.)
And note, most non-MMORPGs games on PC have free online.
Both the PS3 and Steam have adopted their innovations - they've become the defacto standard for online gaming.
These are, as they say, generally the better variety of problems to have, warranty extension costs notwithstanding.
Also, Microsoft envisions Xbox as an entertainment center where families not only play games together, but watch TV and movies as well.
Nintendo and Xbox have claimed different market segments but that's not because they weren't competing.