The only indication that dirt riding makes for better street riding is in the broken minds of those whose broken bodies are veterans of dirt riding while kids.
I'll repeat - there is NO skill for street riding you learn on the dirt. None. Street riding is about lane placement, traffic reading and so forth. Dirt riding is about "if you ain't falling, you ain't learning".
Consider yourself lucky that your dirt riding experience didn't cripple you.
Why be born again when you can just grow up?