I start by stating that I own both. Be careful with the recoil in heavy bullets on the Win Mag...they can be punishing. I opted for a Remy 700 Sendero which greatly reduces the felt recoil compared to a sporter...definately would not recommend a light weight here.
The .308 is a staple that can be used from prairie dogs to elk. It is a great choice if you can only have one gun. Ammo is always readily available as well as usually a large selection too.
My main decision when choosing which rifle is, what is my intended use? Elk, bear or moose, I will take the Win Mag. Anything else and it will be a smaller rifle.
I have shot deer with the Win Mag and it produces bang flops, but it will also creates a pretty big wound. I shot too far forward on a muley at 150 yards and it destroyed the outside shoulder. The shrapnel from the shoulder took out a softball sized hole on both rib cages and shredded the far side shoulder too. A waste of meet. Yeah, it was me and a bad shot, but I believe with the same shot in a .308 it would not have been so devestating.
Thinking it was a fluke and a bad shot that produced such a wreck, I shot my next one in the neck just below the head. Again it produces bang flops, but man, what a mess. It almost completly tore the head off. It was held on by skin only.
I have never used the win mag for deer since....dedicated elk rifle now....which is a role it fills very well. 19 elk and counting.