While I believe the 338-06 to get the nod in over all performance, I see Marlin giving the green light to chamber the Handi in the 338 Federal sooner than I can them doing it in 338-06
I believe 338 Federal would be a great mid range hunting cartridge, and especially in a Handi.
However if it came to getting it done professionally then, I would suggest the 338-06. At first I knew very little about the cartridge, but the more I learned the more I have seen it as an excellent cartridge. Especially in a 26" barrel like Mac and Tim have had done.
Would be it the 338 Fed. be a good idea? Depends on your hunting demands. But either way, it would be a cool one
I don't know anyone that has a Handi in it....yet
-Aaron