Paphos is a lot more "touristy" and picturesque. OK, it has it's dowdy areas, as it's an old resort, but there's also plenty of new/modern. Limassol is a lot more commercial. The first time we went, our rep summed them up perfectly - she said if you want to look at fishing boats bobbing around in the sea, go to Paphos, but if you want to look at tankers and cargo ships bobbing around, go to Limassol!
But having said all that, I'm now a convert to Protaras at the other end of the Island which is a lot more modern and has a lot more going for it such as watersports, etc., and still doesn't have the cargo ships and tankers as a view! The Island is small, so driving to Protaras from Paphos airport isn't too bad, although you could fly into Larnacre instead.