I say this. I'm a native English speaker.
The phrase "since I've seen you" has connotations of meeting and discussion, whereas "since I saw you" implies that I merely saw you in the distance and it refers to a specific place.
For example: "It's been a long time since I saw you at the cricket ground".
This sentence infers NO meeting or discussion. The person may have been playing cricket and I saw him on the field.

