There would never really be any real difference but in certain things you would choose one over the other. You would for instance never say 'I'm bad with chess.' you would say 'I'm bad at chess.' To me there is always an implied missing word. 'I'm bad at (playing) chess.' 'I'm bad with (remembering) names.' I don't know. It's one of those things with loads of exceptions and coming up with a rule is hard for me to explain. Maybe someone else will be able to.

Hi, there's no real difference as far as I know, for example "I'm bad with names" would be the same as "I'm bad at names."