For me it has to be the English accent,I myself have an American accent and I DESPISE it.The American accent in my opinion is extremely boring,The English one just sounds powerful and is sometimes even sexy.
I think my accent is a bit wierd, I still have a bit of a south London accent, but I've been living up north for half my life and somehow it's made me sound a bit posh at times, other times it's just an annoying drone (much like this comment XD).
But as to which accent is better I'd say the English cockney accent is best.
I have a standard American accent with a hint of southern inflection. While I don't have much of an accent, I do extend my vowels and talk slower than people who were raised on the coasts, for example.
My favorite British accent is that very clear, Received Pronunciation that no one - not even newsreaders on the BBC - tends to use anymore. In second place is Cornish. I had a professor who grew up in Cornwall, and I could just sit and listen to him talk all day long. It made Architecture for Non-majors much more tolerable.