For me... I'd probably choose a cat over a dog. I like dogs and puppies, and they're great and they have soul and all that, but I get along with cats a lot better for whatever reason. I can relate to them better.
It's usually people's cats who come to me, but I occasionally have dogs drawn to me as well, and it's usually dogs that tend to not care for company. For example my friend's grandmother's black pug avoids company, but I came over and sat on the recliner, and the dog hopped up and lied down in my lap, facing out like she was guarding for me. I was just like 'whatever, she likes me, petpet and all that' but my friend's grandma stopped what she was doing to stare in astonishment and pointed it out to everyone in the house.
...hm. That friend's cat who only likes my friend's mom actually comes and lays with me too. She doesn't care for my friend or her dad, and she hates company, but she lies down on or beside me, to everyone's surprise. When I want her to come over to me, I just have to look at her and say "mow" and she walks right up and gets in my lap.