I think there is absolutely no case for 'which is better?' because both shows have completely different story-lines and focus on completey different aspects of medicine;
Grey's Anatomy is all about the characters and their 'journeys' through internship. In season 1, they concentrated more on the medical jargon and the patients, but season 2 is now mainly all about their personal relationships, not about the cases,
whereas
House is mostly all about the medical stuff, and hardly ever do we get to see the characters outside of the hospital. The personal stories are only weaved into the show, so they don't lose the part of the audience who isn't going to concentrate on medical technicalities for an hour.
This is evident if you compare the opening scenes of both shows;
Grey's almost always starts off at meredith's house, whereas house always starts off with the patients.
So, I for one couldn't decide which is better, because they're both totally different! I love house cause it's smart, and accurate. And he's mean and hot LOL. And i love grey's cause I love the characters and the wit.
Whichever you prefer depends completely on what you think a medical show should be; about medicine or the characters? (rhetorical question - don't argue this nemore
)