I never put in my 2 cents on this thread so here I go (and I revive thee thread)
It's pretty obvious who my favourite Beatles child is Jason Dhani
I like Dhani's music, his personality, the fact that he looks like George isn't a bad thing either 
He's closely followed by Julian though (daww Julian seems like such a dote) if I liked Julian's music he would be seriously competing with Dhani but I think Julian's music has aged quite badly, sorry Julian :/
Julian "made it" in the music world but he isn't really listened to ...