While I cannot speak directly to the 375/06, 375 Whelen, 38 Whelen, all the same cartridge, I do have both the 35 Whelen and 400 Whelen. My gunsmith friend who made my 400 Whelen made a 375 Whelen for another friend of mine. He loves it and has had no trouble tipping moose over with it.
It certainly is not in the class of the 375 H&H or 375 Ruger but it is assuredly adequate for anything in North America, or elsewhere for that matter. One of my next builds will be the 38 Whelen, and it will be so marked as that was the original designation for the now 375 Whelen. I surely don't need a 38 Whelen with both the 35 and 400, but as a Whelen fan it seems appropriate to have all three standing next to one another in the safe. Mine will wear a 24 inch barrel like it's brothers.
PO Ackley lists loads with a 235 grain bullet to 2600 fps. Mike Thomas in "Wildcat Cartridges" list loads with a 270 grain bullet to 2410 fps and 300 grain bullets to 2185 fps. I expect Ackley's 2600 with a 235 grain bullet might be a bit optimistic but I could be wrong. At any rate those velocities make the 375/06 a formidable big game rifle.
I do have to agree that the 375 H&H and Ruger make more sense from a practical stand point but all the cool guys have at least one Whelen in the safe.
Shooting a wildcat with some history to it is fun, or at least it has been for me. When I go to the range with the 400, guys always ask me about it and and are amazed at the size of bullet seated in what used to be a 30-06 case. It makes for some great conversations and some times new friendships. If you are up for a fun trip down the wildcat lane, I don't think you could go wrong with the 375/06.
Mart