Dre,
Perhaps I have the "recoil sensitivity" of a mule but I own essentially identical Model 760 rifles in both .30-06 & 9.3x62mm (that Jessie at JES reformatted) & I can tell little/no difference in the "kick" of the two calibers.
(Actually, I have 3 Model 760 rifles in .30-06, as the Model 760 rifles seem to "keep falling into my lap" at estate/garage sales. = Right now I have 8 Model 760 rifles/carbines in .223REM to my treasured 9.3x62mm.)
Note: One of my "garage sale" pump-rifles is a .30-06 that has a badly pitted barrel.
(The PO shot a lot of cheap/corrosive/surplus service ammo in it & evidently W/O ever cleaning it properly.)
That pitted rifle will soon head to JES to be "reborn" as a .400 Brown-Whelen Improved, which is the most powerful wildcat cartridge that can be formed from .30-06 cases. - The "BIG .400" is the "ballistic twin" of "the well-regarded in Africa" .404 Jeffery, that has been used very successfully on every species of big/dangerous game there. - The .400 B-WI uses the same cast/SP/solid bullets as the .405WCF does.
(Truthfully, I don't need a BIG-bore rifle; rather I just want one & a reformatted 760 in that caliber is A-OK with me for anything that I'll ever hunt in this life. - The .400 B-WI "pushes" rather than "kicks", in the one 9.5# rifle that I've shot in that caliber.)
yours, tex
