Mice are sweet little things, but rats are definitely more personable. I think it is because they are bigger. Mice can enjoy being with you, or at least not mind it, but my ratties will come bounding up to me and beg for cuddles. My boy Hyde was such a cuddlebug that if I just put him down on my lap, he would prop his forepaws on my stomach, headbutt me and stare up at me until I'd pick him up and kiss and cuddle him. At which point he would boggle his little brains out in delight.
I've never had mice myself - my experience has all been with friends' mice, or from my rodent-loving vet regaling us with her tales, but from what I hear tell a mouse will smell more. I've trained my rats only to poop in the litter tray (mostly) and not go on the carpet (mostly) so that helps. :)