Just some back-of-the-napkin calculations:
1-10x10 post = 100 sq in
1-2x6 stud = 12 sq in
So each post is equivalent to 8.33 studs.
At 16" on center, the studs will go 133" or about 11 feet. That's pretty close to the spacing you might use between 10x10 posts. Using 8x8 posts, the timbers come out ahead if the spacing is merely 7 feet. Granted this is the simplest case. I didn't address trusses or compare plates to girts, etc. But I think it's fair to say that you're "in the same ballpark" with repect to the raw amount of lumber consumed. Now to be fair, you also need to acknowledge that the timbers require bigger trees, and thus will take longer for the forest to replace, but I think that's more than balanced out by Timberbe's point: the timber frame is built to last for many generations.
