The 7mm Rem. Mag. and 270 Win. are effectively the same "caliber" (bullet diameter).... difference, obviously, is the cartridge case. The 7mm Rem. Mag. much larger case and therefore is loaded with substantially more powder charge. It is one of the best selling cartridges developed by Remington. Most folks I know that use this round for deer prefer the 150 gr. bullet weight.
The 270 Win. is one of the best and most popular rounds for deer sized game. It is a 30.06 Spr. case necked down to 7 mm. It handles a 130 gr. bullet superbly. You could not go wrong with either.
As for recoil, if you are comfortable shooting a 12 ga. shotgun load, then you are plenty good to go for a 7mm Rem.