*What is the difference between...
One thing to note: I've never said, "Let's go Dutch." I also don't know anybody else who's ever said it. I've only ever heard, "Let's split the check/bill." It's very natural and will be understood by everybody.
If you're trying to say, "Each pay their own way," just say that. "Let's each pay our own share."
(For reference: I'm in my 30s from the northeastern US.)