Either cartridge will fit the bill for anything in North America. It really just depends on what you want. I personally would go with the regular 300 Win mag, I like to shoot heavier bullets out of magnum rifles, and the longer case will do a better job with 180+ grain bullets. If you don't handload, it should be easier to find ammo (and possibly cheaper) for the WM also. And there are lots more used rifles out there in WM since they have been making them for much longer.

Recoil is going to be very dependent on the gun, stock design and gun weight will make a big difference in felt recoil. Recoil between those two cartridges should be almost identical - one uses less powder so it should recoil a little less (WSM), but the other one will most likely be in a little bit heavier rifle (WM).

My main deer guns are a Sako 75 7mm STW and a Remington 700 30-06. According to the calculations the STW should have 50% more recoil than the '06, but you can ask anyone who has shot them, the Remington hits harder. The stock on the Sako is much more comfortable, and a little heavier, so even with more recoil, it is more comfortable. Neither are even close to a buddies single shot 10 gauge turkey gun. That thing will bring a tear to your eye.

Jason