Is it just a matter of unplugging the cable (from the antenna end) and popping it into the RFX-250?
Yes. I was just making you aware of the pinout if you were or plan to extend the antenna farther since your existing antenna does not have a molex connector. Plug and play with your existing setup.
Oh, by the way. Will the range be improved (comparable to the older remote)? Or does the narrow band RF just have shorter range?
Range should be slightly better than your old setup but that's really a factor of the systems' environment and antenna placement. The real purpose of the rfx-250 is the narrow band for filtering out interference in the 418 or 433 MHz channel which amongst other things can reduce range and reliability.