I think they call them the HD twins cause they are practically swappable. They have the about the same power, graphics and games that the other. There are a few exclusives, but that's about it. Sure Sony has better storage (blu-ray - but what like 3 games us it?) and Xbox has a better online service (that you pay for), but those are the differences.
But even the CPU's were designed at the same time, by the same company (IBM).
So if you got and X360 or a PS3 you would open yourself up to many of the same games. But if you had a Wii you could have a completely different gaming experience (with motion/movement.)
Having owned a 'Le Stick' in the 1980's I'm was amazing Nintendo was able to pull it off and make it fun.