This was a similar question that I asked TBAC when seriously researching am Ultra 9, which I now own spanning a .308 and .223 rig due to their CB brakes.
I was told in an email conversation with Ray Sanchez of TBAC: "CB brake mount is the way to go for a precision rifle. Its a better mount than a direct thread. The shoulder on the back of the brake is way better than a 5/8 or even 3/4shoulder can offer."
I think it's a matter of the surface area provided by the base of the brake and resulting torque "snugging" up and holding things secure vs just the threads of a direct. I know this is a rather vanilla description, but intuitively it seems to makes sense as providing a better seal.
He provided these vids to demonstrate how boss he is and of course, why the CB's a better option:
Here are some videos that show how good the mount is
Here is a link to a short video that shows some accuracy and repeatability testing of the CB mount on a 308 at 700 yards
https://thunderbeastarms.com/news/30cb9-accuracy-and-repeatability/
Here is another video of a 6.5 Ultra on a 260 with a CB mount at 700 yards just to show how good the mount is.
Hope this helped and enjoy your TBAC whatever you choose.