To me, they mean pretty much the same thing. "That's it" is more flexible, though- it can come at the end of a conversation or discussion, sort of to say, "So, we agree," or "That's how things are," (this is when "That's it" and "That's that"), but you could also say, "That's it!" if someone guesses an answer correctly or does something right. If you said, "That's that!" in that context, it wouldn't make sense. I hope that's helpful- this is a pretty specific usage question.