When you start comparing apples to apples in terms of BCs the 7 tends to be a hair flatter and carry a hair more energy than 30s. With the 175gr LRAB in the 7 Remington and the 210 LRAB in the 300 the BCs are about as close as you can find for comparison sake. They also start out darn near dead even in muzzle velocity (according to Nosler) which translates to a whopping 6 extra foot pounds at a grand out of the 300. With about 100 yard zero the 7 is 1.75 incles flatter but in a full-value 20mph crosswind the 7 deflects 1.75" more at a grand. Does that matter when you're dialing? Not if we're to believe all the BS that 6.5 CM fans spew about.
But where the 7, apparently, beats the 300 is recoil. Using the two loads from Nosler that I used above, and a theoretical 12lb rifle, I punched the numbers into a recoil calculator. Surprisingly, the 7 recoils just under 17 ft lbs and the 300 recoils at a smidge over 25 ft lbs...pretty much half again as much! I guess that's the difference in 35 grains more bullet and 16gr more powder.
So without actually shooting this theoretical rifle, it appears that it would be a lot more pleasant to shoot in a 7 than a 300. That being said, our 12lb 300 is only going to recoil a touch more than a 9lb 30-06 with 180gr Partitions which is a pretty docile load by gun nut standards. Other than that, it doesn't appear to make a damned bit of difference.