I'm going to catch you and I'm going to catch up with you have two different implications. To catch you means the speaker is chasing the person he's speaking to and wants to grab him or that the speaker is an authority figure, like a police officer, who's trying to catch the person in a lie or crime. To catch up to means the speaker is trying to reach the same place as the person he's talking to.
Disagree, while they both can be used that way it's certainly not limited to that usage. In fact I'd go so far as to say that using catch up to is uncommon.
For example when racing someone it's common to say I'm going to catch you. There is no intent to actually have any physical contact. The "up to" is often unspoken as it's clearly understood without it.
These are probably regional variations. In the so-called "American Midwest", where I live, I would always say "I'll catch up to you" in a situation where I'm racing someone, and I would only use "I'll catch you" if I was chasing someone. Basically, in my area, "I'll catch up to you" is by no means uncommon. Using "I'll catch you" in a racing situation sounds British to me. Are you from the UK, Luke?
OK, so you have an explanation as to different meaning. How can you tell out of context whether the phrase is "I am going to catch you", or "I am going to catch up with you.". I concur with many ofthe other comments that I am going to catch you is the more common response here.
To catch up with someone has a different meaning than to catch someone up. I am going to catch up with you is like, "you start walking down the trail now, I'll leave in a few minutes but I'll catch up with you" Catch you up is like, "You missed the first ten minutes of the film, I'll tell you what happened to catch you up"
I am going to catch you up would mean I am going to brief you on something. As in catch you up on what has been happening. Very different meaning from I am going to catch up to you. Alcanzar also means reach, so to say I am going to reach you, or "catch up" to you means the same thing here basically...
There seems to be a problem with these lessons that I have not encountered before. Whatever response is entered for the last statement/question of a series (of five questions) is repeated as the response in the first question of the next question in the series when the new series opens. (i.e. Question 5 response is repeated as Question 1 response in the next series but cannot be overwritten or changed.) Duolingo has crashed a few times in the last few days, and it looks as if there is still a problem. Nothing like this occurs in any of the other applications I use on any given day.