Hi, I am not an English teacher, but as a native speaker I will comment. The two sentences actually could have very different meanings.
"I'll catch you." means "I will capture you"
ex. The policemen yelled at the escaping burglar, "Someday, I'll catch you!"
"I'll catch up with you." can have two distinct meanings:
1. to overtake or draw even with someone, as in a race
ex. "You are ahead of me in speaking English but someday I'll catch up with you"
2. It also is an idiom meaning to hear the lastest news or gossip from someone, to have an informal conversation.
ex. "I can't talk now, but I really want to hear what happened at the party. I'll catch up with you tomorrow." {we will have a conversation about the party tomorrow}