完 means finished.过了 means have done

To me, both of them mean different things. 我吃过了 means 'I had a meal already / just now' while 我吃完了 means 'I just finished my meal'. I have never heard people saying '我刚忙过了', it doesn't really make sense, but 我刚忙完了 is very commonly used to express that you're free now after completing the work.