HI Vivian, a hard question..
I would say..
yes, there is a difference. the regular form (..eru) is called the potential form and is used for simple possibilities, like 'I can play the piano', 'I can go tomorrow' or 'Can I pay by credit card?'
If you use the other thing (koto ga), it sounds too formal or more serious, like the possibility of doing something doesn't exist. It's not usually used for those simple things in my experience, except if you want to say that something is really possible or not (because just saying 'I can/can't' can mean that you don't have the chance to do it)