Having a dog and cat that hate each other would be pretty bad. Having a dog and cat that adore each other would be pretty cute, but after a while you would just take it for granted that they were always snugsy-wugsy. It may even be a little cloying.
Having a dog and cat who are quite fascinated with each other, but are still working out the power balance in their relationship - that's comedy gold. The double-take, the double-double-take, the slow burn, the fake insouciance, the completely-boneless posture betrayed by the darting eyes - it all leaves Ross and Rachel's travails in Friends for dead.