Apple Watch will unlock one MacBook but not another

Are both of these devices signed into the same Apple ID? Have you tried turning off the feature on the Macs, then turning off the Macs and turning them back on again. Then setup the unlock again? Unlock your Mac with your Apple Watch - Apple Support See the "Learn More" section about troubleshooting.

I know there are a couple of other threads about this. I've only experienced an issue with mine once, and following the steps in that support document fixed mine. You can try searching for the threads here if you wish and see if anything there helps, you can try posting in one of the Mac forums that match your computer information and see if anyone there can make a recommendation, or you can use the Get Support link a top of the page here to contact Apple Support.

I've never read about unpairing and pairing again. But I'm guessing that you did follow the steps in the Learn More section of the document I provided?