Unless you are worried about exceptionally long range where the slightly higher BC of the 6.5cm will start to outweigh the initial velocity, 7mm-08 is a bigger, more capable cartridge than a 6.5cm, it's going to push the same weight projectile at about 100-150fps higher velocity and is available in some heavier bullet weights if you want that. I really like my 7mm08, current rifle is a tikka. Between me, my brother and my wife as well as a few friends, it's cleanly taken elk, moose, and many deer and a solid handful of antelope.
That said, it's still typically a 140gr bullet pushing 2800- 900fps, so if you get a really lightweight rifle it's going to kick unless you opt for a lighter bullet or lower velocity. My wife finds 140gr ammo uncomfortable to shoot out of her lightweight rifle, so for deer sized game typically uses 120gr reduced recoil ammo (about 2600fps), and has taken deer and antelope with this just fine. It's a pretty popular cartridge I'm told, but still not always easy to get ammo in lean times like now. My 7-08 rifle is abnormally finicky about ammo and I'm having trouble finding something it'll shoot well right now. At least around me, 6.5cm is overwhelmingly easier to find on a consistent basis. At the moment, between 4 local shops I have my choice of winchester ballistic silvertips and nothing else in 7mm08, or I can choose from multiple brands and bullet weights, in both lead or copper, bonded, varmint, target, etc bullets in 6.5cm. I also have not been able to find any of the ammo my rifle likes online in 7mm08. Absolutely nothing wrong with 7mm08, it's one of my favorite cartridges, but if reduced recoil and ammo availability were chief concerns I'd lean toward a 6.5cm.
edit: I also missed part of the questions, and I agree 100% with the post after this one, except I'd add .308 to that list