Sometimes there is no difference. Sometimes there is! Examples: I've got to catch up on all this work. I've got to catch up with all this work. Either way, I'm on catch-up! Oh dear! All that work! But with people it's only catch up with. I've got to catch up with my friend (he's ahead of me, walking faster). And we also use it to say 'see you later sometime' as in 'I'll catch up with you next week maybe.' or 'catch up with you later at the cinema.' I have work to catch up on now so catch up with you later, ok?

"Catch up with" is usually a situation when you are chasing someone who is in front of you and you are trying to get to the place they are.IT is a physical race. "catch up on" means you have fallen behind.For example if you missed a couple of lessons and you don't understand the teacher you need to study alone to get to the same place with the rest of the class.So you have to "catch up on" your studies.

For me, 'catch up with' is used with animate objects and is used primarily to talk about meeting and/or talking to someone. "I need to catch up with my roommate from college." This means we haven't seen each other in a long time, so we need to learn about how our lives have been by talking. 'catch up on' means that you are behing on something and need to be current. "I need to catch up on Big Bang Theory." This means that the newest episode is farther ahead in the series than the episode I need to watch. "I need to catch up on my work." Same idea; you are behind on your work and need to fix that problem. I don't personally use 'catch up with' in situations where I'm chasing someone or something. I would say 'catch' if I'm literally chasing with the intent to capture. If I'm chasing a running mate, for example, I would say, 'catch up to'.