Gatwick is in many ways better than Heathrow, it's got a nice feel to it. I've never connected to another flight at Gatwick, so I don't know about that - but I do know Heathrow can be a hassle.
Best of the bunch though is Stansted. Compact, clean and friendly. All three airports have good connections to London. I've not been to Luton, which these days is the new destiantion for Scandinavian charter flights to London.
Trains and boats and planes....