Unfortunately, it depends on the context. If you're talking about a specific admission/acceptance at a specified time, then it's the first one in both examples. If you're speaking more generally, without specifics, and the admission/acceptance has relevance in the present, then it's the second one. Perhaps it might be helpful to look at it this way to see the difference between the two: You admitted (yesterday) that you did that. You've admitted (at some point in the past) that you did that.

All of them are correct... "You admitted that you did that." = It's past simple and means that at some point in the past you admitted that you did something. The past simple signifies a completed action in the past. "You accepted that you did that" = See above /\. With verbs in this form (the past simple), you can phrase the sentences as follows: "Yesterday you admitted that you did it". "Two weeks ago you accepted that you did this." ---- "You've admitted that you did that." = This is in the Present Perfect tense, which means that it happened an unspecified amount of time before now. The tense is often used to express a change over time. So, for instance, in a police interview room, the person being charged might have been lying for some time and then finally told the truth. Due to the change, "You've admitted that you did it" would make sense. "You've accepted that you did that" = Fine. With the Present Simple, the following types of sentence are WRONG: "Yesterday, you've accepted that you did that". = The tense is ALWAYS used for an UNSPECIFIED time in the past. ---- Hope this helps :)!