My manuals tell me that the "mildest" 7mm family is the original, the 7mm Mauser, or 7x57mm. I won't call it weak, 'cause that round has killed big game all over the world, and was hailed by a number of pretty savy shooters.
Apples to apples, the 7-08 gains about 200 fps or so on the old Mauser.
The .280 is a dandy round, but its caught in the nether world between the .270 and all the .30 cals. The .270 is so well established, and the cartridge does such a good job on deer sized game, that the .280 is a sort of afterrun. And if faster and flatter is what you want, the round that gets it for most is the 7mm Mag.
I don't own a 7mm rifle either. But if I was so inclined it would be a 7-08. The short action and the recoil reduction from .30 caliber seems appealing.