Recoil Question - Different Caliber but Similar Charge and Bullet Grain

[Bidwell]

Been considering different calibers for a new lightweight rifle. I'm just using Barnes 130 ttsx copper bullets and maybe some 110's for my 308. Looking at both 308 and 6.5 cm load data, you can use similar charges for both, albeit different powder. Would recoil be much different for either rifle if charge and bullet weight are roughly the same? This seems like a Newtons third law scenario to me, so feel like the recoil should be close-ish. Does bullet diameter make any difference here? Only difference I see in the load data is the 6.5 will be a couple hundred fps slower than the 308. I've never been able to feel the recoil difference between something like 2800 fps and 3000 fps. If I'm only shooting out to 300 yards, maaaybe 350 max, are there many advantages to the 6.5 other than slightly less drop and wind deflection? I hear the 6.5 is inherently more accurate, and others call bs on that, so I'd like to hear any opinions on this too. I have no experience with it.