In daily talk, 顾得上 has some subtext, like "although I'm busy, I still put you(or a thing) at high priority and be able to deal with it.". This expression is not only to show you have capability to achieve something, but also to show that you take it seriously.
顾不上, as an opposite expression, also has its subtext, like " comparing to other important things, I give up/ignore this one(at least not for now)".
here are examples:
btw, would you like to revise my written words above? I'm an English learner :-P
thank you! an interesting question.