I've own both the .243 and the 7-08 and while I've killed a lot of deer with the .243 and all but one was DRT. I've only killed a few with the 7-08 but had the same results.So I would say you're correct. But the 7-08 have a more KE. And comparing sectional density and ballistic coefficient of, lets say, a Nosler Ballistic Tip the 90 gr 6mm has a SD and BC of .218 and .365 while the 140 gr 7mm is .248 & .485 making the 7mm a much better bullet for longer ranges. It's hard to say that recoil is the same because they are two different manufacturers. But even then, recoil, even of the same model varies from rifle to rifle. I've witnessed this first hand. Any variation in butt angle can alter the felt recoil. But with the same case the bigger bore IMO negates the heavier bullet making recoil feel pretty much the same.
As for you shooting at least 300 deer! Wow that's almost 9 deer a year. You've either got a very large season limit where you live or you're shooting them for someone else. But IMO that's more deer than anyone should shoot and utilize. I understand that you like almost all of us love hunting. But there is I fine line between sport hunting and greed just to satisfy an ego. I personally shoot no more than 2 deer a year. And even at that and eating it in some form or another at least once a week, its more than enough for my family.