Either will be good, but a 7-08 shooting 120s or less is a 243 for all intents and purposes, including recoil.
I disagree.
Having owned both a Kimber Montana 7mm-08 and a 243, the 7mm-08 with full power 120s is a considerable step up in recoil from a 243, especially in a light rifle like the Kimber. A Kimber 7mm-08 will come back at you pretty fast, and it wouldn't be tough to scope oneself with a light hold while firing full power loads.
In comparison A 243 can be loaded with a bullet like the 80 grain TTSX at around 3000 fps, and be a real pussycat to shoot, while still maintaining a nice trajectory.
