I routinely shoot a couple of my 7mm08's at 700 yards on the 16" gong. For whitetail I wouldn't push the round further than 400. For Elk, 350 with a choice pocket shot. You could push the 7mm WSM further with a heavier bullet and cranking up the load a bit. As Uncle said, the case capacity is a bit larger for the WSM so you can get more powder in there for a larger bullet but once you past around 160gr bullet weight the length of the bullet will take up case capacity for powder.

Since you are new to shooting/hunting I doubt you will be jumping into reloading your own ammo so you will want to look at availability of factory ammo. 7mm08 is highly popular all across the country and I think the 7mm WSM is kinda losing steam with the masses. I may be wrong in that assumption and since I haven't bought any factory ammo except a box or 2 of something I needed right then in over 40 years I have very little knowledge of what the stores commonly have in stock for factory ammo.