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The 338 Fed shoots the same bullet weights 50-100 fps faster than a 308 and 50-100 fps slower than 30-06.
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The Federal is a little better cartridge than you are giving it credit for. I'm a .358 Win man myself, or I might have the Federal in my safe.
If you stick with factory loads and data the .338 Federal shoots a 210 grain bullet 60 fps faster than a .308 with a 180 grain bullet, and 70 fps slower than a .30-06 with a 180. With a 185 grain bullet a .338 is 50 fps faster than the standard 2700 fps for a 180 grain .30-06 load. With the 210 grain bullet the .30-06 doesn't match the energy until 300 yards and they stay pretty close at 400 yards, and the trajectory of the 210 is equal to a .308 with a 180 out to 400 yards.
Even dropping down to a 165 grain bullet in .308 it doesn't best the Federal with a 210 grain bullet by much until you get past 500 yards. The .338 Federal will still have more energy, and a 3-5" more drop at 500 yards. The Federal is in its sweet spot between 200-400 yards. You're right about the .30 cals offering more penetration however I don't think you'll have issues with the .338 Federal and penetration through tissue and bone using a 210 grain Nosler Partition.
(All comparisons were taken from Federal Cartridge 2013 ballistic charts. All bullets were chosen on similar construction or BC except the 185 grain bullet. 180 & 210 grain bullet comaprisons were Nosler Partitions, 165 grain bullet Sierra GK, 185 grain bullet listed as "Soft Point".)