None.
Both of these verb tense forms refer to the past. There is a very slight difference in meaning.
To explain the difference, I'm going to be ridiculously precise.
Suppose you had lunch with someone from 1:00 through 1:29 and then got up at 1:30 to say goodbye.
"It was nice to meet you" means you are thinking of lunch as a single event. You are thinking of the number one: one lunch. And you are putting it entirely in the past. It included 1:00 through 1:29. It is now 1:30 and it is over. You are thinking of the number "one," one lunch.
"It's been nice meeting you" means you are thinking of a period of time, 31 minutes, 1:00 through 1:30. Although you are at the very end of the period of time, it is not quite over.
To me "it's been nice meeting you" is a little friendlier, because the "nice meeting" is still happening, whereas "it was nice" means it is over.
I'm not a grammarian and had to look up the names, but that's the difference between the simple past tense ("it was") and the present perfect continuous ("it has been.")