It all depends on the species fighting.
For example, domestic cat vs. domestic dog(large dog)= Dog winning because of it's size and strength of its muscles. But, if it was against a smaller dog, the cat would most likely win because of its sharper teeth and claw.
Another one would be: Big cat(lion, tiger, jaguar etc.) vs. Wolf= Big cat wins because of its strength and size over the wolf.
Domestic cat vs. Wolf= Wolf wins, obviously, because of its larger size, strength, and stamina.
Big cat vs. domestic dog(large or small)= Big cat win since its so much larger, stronger muscles, and bigger jaws meant for killing.
So, basically, it all depends on which species you are referring to. However, if I had to pick one of the two, it'd probably felines because there's more of a variety to the species and they tend to be larger/stronger than the canines. As much as I love canines, cats do have sharper claws/teeth and there's more species that are stronger and faster than canines of any kind.