There is no real difference between them. To say "I look forward to talking to you soon" is to say how you feel about talking to someone generally. To say "I am looking forward to talking to you soon" is to say "right now at this moment i feel good about talking to you later because I expect that it will be good." But it's not that serious. You can say either phrase and it will be correct. Although, I will say that "I look forward to talking to to you soon" is the more natural thing to say. But it really doesn't matter. An English speaker will understand what you mean and it will be correct.

"I look forward to talking to you" = This is used in the general sense; I'm always happy to talk to you. NOTE: "I look forward to" is in the present simple tense, so we do NOT use "soon" here. But, in the next sentence "soon" is appropriate because it's planned in the future, and there's not much time left to wait. "I am looking forward to talking to you soon" = This is used when there is a planned appointment coming up in the near future.