The book rationale is that in cost plus you are bearing more cost uncertainty, and in fixed price the GC is bearing more. But, for both, the change order process is their way to recover most unforseen issues. It all boils down to the quality of the GC and their subs.
But, for empirical data: a significant remodel in Seattle about 5 years ago was cost plus. We uncovered lots of issues so the scope exploded. Fixed price would not have been much help there. But, the productivity of the GC's own guys was too low. Put some productivity terms in your contract.
An even more significant remodel in FL last year went fixed price, with the largest GC in town. They ended up being as professional as I was used to in industry. An 8 month schedule ended up 9, due to having to stop for a hurricane. Cost came in just a tad under bid, and I got that difference, due to the contract. This job was 3x the size of the Seattle job.
If schedule is not that critical, your brother plan can work, if you put a whole lot of attention into it, and incentivise him appropriatetly through a contract.