To further explain my comparison of the 30-06 & 338-06 as support and to answer one of the points you brought up about "air" slowing down the bigger bullet.

I utilized Norma's ballistic calculator to come up with some figures. I compared Nosler Partition bullets at 2600 FPS for the 30-06 and 2700 FPS for the 338-06. Nosler publishes the BC of the 30 cal 180 gr partition at .474. I was unable to pull the bc of a 200 gr. 338 cal partion so I used the bc of a 225 gr the 200's bc should be better than the 225 so I feel confident in my numbers. So KE numbers are as follows:

Muzzle--> 30-06 = 2700... 338-06 = 3200 +500 ft. lbs.
100 yds->" = 2300... "= 2700 +400 "
200 yds-> " = 2000.... " = 2300 +300"
300 yds-> " = 1700... " = 2000 +300 "

The 30-06 is very similar to the 308 so by association I believe the 338 federalwould be very similar to the 338-06. It is fairly reasonable to assume that the numbers would have a very distinct correlation.