Ben Law have his general rule of thumb for his wood. He says that round timber is 50% stronger then the square milled wood you could get from it.
I have heard this before from other sources, but never any data to confirm it. Does he mention a source for that claim, or is it merely his opinion based on experience? 50% is a lot. It may be true, but I think it depends a lot on the species of wood, as well as how it is prepared and in what position it is used in the construction. As a quick example, I could mill a 4x4 from a straight 5.5” log. Was the 5.5” log 50% stronger? How does one determine that? Is the use vertical, sloped or horizontal? The end use matters the most.
It’s also not typical to use much square milled wood, other than vertical posts. Most construction is done with lumber that has a rectangular profile (2x4, 2x6, 3x12, etc). Horizontal members such as a header or joist bear the most loads at right angles to the fibers of the wood. So in a position where you may want, say, a 4x8 support beam, the 10” log it would take to mill that beam will easily be twice as strong, but that’s also because you could get 2 of those beams from that log (nominal lumber sizes. To get full 8” would need a 12” log for 2 beams). So it’s overkill for sure, but also a lot of extra resources and weight. On the other hand, it’s simpler to peel logs than to mill them.
I think you’ll be fine with round wood, especially with a 12/12 roof pitch.