Grey's Anatomy is much more of a comedy. House is a drama, period. House is much more focused on the medical stuff, Grey's is focused a lot more on the relationships and whacky situations.
That's exactly why I like House. Because House is a medical show, not a damn soap opera. Yes, there is some relationship drama in House but it is about 85% medical, 5% Comedy, and about 25% medical-related comedy. that leaves a measely 5% of soapiness. House is awesome and Hugh Laurie is an awesome actor.