Hmmm…Are you working either job already? Based on your original post it looks like you have not started the Federal job yet.
Entering the adjudication process does not necessarily mean you have the clearance yet. If you are working before the process was completed you may have been granted an interim clearance.
With the defense contractor sponsoring you for secret that means you will fill out the SF-85P now instead of the SF-86 you already completed, which means an entirely new and different investigation.
If it were me, I would take the new offer from the defense contractor. I would ask them if you can start working immediately or have to wait until their clearance is completed. Besides the mass elimination of Federal positions going on currently, if you have not started already, you just do not know when you might start. With it already being a year gone by one would hope it would not be much longer, but I know people who waited over a year to get started.
That said, what potentially could happen is you take the private gig, start that job, and after you start the private gig, the federal job comes through. To me it would be better to have a job already and then decide if I want to switch, instead of waiting on a Federal job that may or may not materialize.