Personal preference, mostly. I just think Customs look better.
For the same reason that, out of two bikes, same model, same year, same everything, the RED one is always faster!!
You ever seen those heavily accessoried Harleys? The big Fat Boy models with all the chrome, the white leather and the tassles on everything (seats, saddlebags, bar ends, even floorboards)? The bikes look like frickin' Elvis in his white suit!!
Well, Classics with their looooong sweeping mudguards and heavy accenting seem one step down the awful road toward having an Elvis for a bike, to me!
Nowhere near as bad as that Kawasaki one, but still not to my taste.
However.... The 650 Classic does have about 20kg (or was it 50kg?) extra weight, thanks to the metal mudguards and beefed up seat, fork shrouds and other chunkier accenting.
So, technically, you could argue that the lighter Custom has slightly better performance... technically.
End of the day, fuck what anyone else's opinions are - ride what makes you happy!!