I tend to leave stray cats alone, since you can never be sure when their owners might be about. An elderly uncle of mine had a big chunk of land in south Mississippi and kept a kennel full of beagles. When a neighbor's cat showed up, he'd do his best to hunt it down and kill it, much to my aunt's dismay. His hounds were field-trial dogs and his excuse for going after the cats was that they left scent trails that distracted the dogs.
He mended his ways after following a cat to the edge of his property and, intent on shooting at the cat, failed to notice the old lady who owned the cat stepping out on her back porch with a shotgun! When she started screaming at him, he forgot all about the cat and decided to beat feet away from there. He was a bit too late, though. The irate old woman threw that 12-gauge to her shoulder and hit him with a load of rock salt! She was plainly trying to hit him where the sun don't shine, but he was a bit too fast. Instead, the back of each leg caught several chunks, right through the heavy denim pants. I reckon he got what he deserved.
I've had both cats and dogs as pets, both are interesting in their own unique ways. The interesting thing about cats is that they retain all that wild instinct and capability, yet still want to sleep in your lap. Dogs are either docile and domesticated or completely wild, no in-between.