"Since you've been gone" = during the time that you've been gone, up to the present (implying that you are still away, or have just recently returned). "The house has been quiet since you've been gone." "I've watched a new movie every day since you've been gone." "Since you've gone" sounds a bit unnatural. As JmmiP says, it would be better to say "Since you left" or "Since you went away." The meaning of "since you've gone" is still "during the time that you've been gone," but the implication is that you have gone away either permanently or for a very long time. "Since you left" is more neutral, and doesn't imply anything about how long you've been gone, or whether you're still away or have now returned. "Since you've gone" could also be understood as "because you've gone." To me, this seems like the more obvious way to understand this phrase.

To add some context and make it more simple, I'll both to a sentence: Since you've gone to the store, I just played some games. Since you've been gone, I just played some games. Both sentences, in this case, have almost the same meaning. However, the first one you have to add where the "gone" leads to: gone out, gone to the store... etc, you cannot leave that without context, otherwise, it would not be grammatically correct. Since you've been gone just implies that the person left, but it isn't grammatically necessary to mention where to.

I think "Since you've gone" can sound a little unnatural, potentially. It's perfectly grammatical, just a bit formal for everyday conversation. A good alternative would be "Since you went," or maybe "Since you left," if this is casual speech. Concerning the difference between them, they denote the same thing, more or less. Although, I feel like "Since you've been gone" might imply a much longer period of absence, while "Since you've gone" implies a more recent departure, though that's just hunch, I suppose. I'm not a teacher, but I hope that helps!