The difference is not huge, but I think rather it is contextual. Literally, in the first one, you had a conversation with someone. The conversation is now over, and you are commenting that you enjoyed it. There is a sense of finality.
In the second one, there is an implicit signal that something is going to continue. That something could either be the conversation itself or the relationship with the other person in general.The sentence standing alone doesn't tell us what. Maybe the conversation is going to continue, or maybe you are about to ask the person out on a date or something.
- "It was really nice talking with you. Let's do it again sometime."
- "It's been really nice talking with you, would you like to do it again sometime?"
First, I prefer to talk "with" someone, rather than "to" someone. The "with" is better here because it emphasizes that talking is something you do in a pair rather than by yourself.
On a more subtle level, in certain contexts, I might question the sincerity of the person in 1. Does he really mean that he wants to do it again, or is he just saying that to be polite? On the other hand, there is no mistaking the intention of the speaker in 2 -- this is a direct question! I think native speakers often play with frases like these to either indicate an implied desire for finality or continuity, and to be polite. The finality of the statement in 1 is unusual if the true intention of the speaker is for the relationship to continue.
I'm sure other people will have different feelings about this.