Well, I've never had a cat as a pet so haven't bonded with one that way, but I have felt somewhat connected with various cats in the past. A while ago some of my neighbours cats came round during the day to be fed and played with. One cat in particular came round for years and we developed a close bond with her (even before I had a dog). When she was about to be taken to the vet to be put to sleep I was that upset I couldn't bare to see her before she was taken there. And as I said, my sister has a cat now too, and while she is away my mum and I go to her house to feed and let him in/out, and also play with him for a while. He knows who we are because we go to her house every week for dinner.
So yeah, while personally I feel I can bond more with dogs (purely because I haven't had the chance to own a cat as a pet. The reason for that is that my mum doesn't want cats in her house ) I do still think you can develop a deep connection with a cat.