Hi Larry,
Both are great 30 caliber cartridges and both will more than manage all North American game less Alaskan bears. Both cartridges are true 400-yard killers as well. Now here is where there are differences:
The .308 Winchester is arguably one of the most versatile cartridges ever developed. It is inherently a more accurate cartridge than the 300. The .308 is built on a short action allowing for a lighter and more compact rifle if desired. The .308 has quite a bit less recoil than its big brothers (about 18 foot-pounds in a 7.5 pound rifle), its easier and cheaper to hand-load, the ammo is more available throughout the country and the world for that matter. In my opinion, it’s one of the best North American hunting calibers available.
Both my son and I have killed quite a few elk with a .308 as well as deer and pigs. It dispatches game with amazing efficiency.
The 300 Win Mag is a proven 30-caliber magnum and over the years it has become the most widely used 30-caliber magnum in its class of cartridges. It was introduced in 1963 and has become one of the more popular elk rifles in the field. It is accurate and has a good bullet selection. The ammo is easy to find as well. Rifles for this cartridge are built on a magnum action.
The 300 Win Mag produces about 26 foot-pounds of recoil out of an 8 pound gun. While this is not unmanageable, too some folks it is uncomfortable at best. The rifle will need a minimum of a 24” barrel due to the amount of powder the cartridge uses (typically about 75 grains of powder). Like any magnum, the cartridge shines beyond 400 yards and shoots the heavier bullets more efficiently than standard cartridges of the same caliber.
Now here is an opinion based on facts:
If you are hell bent on a magnum in .30 caliber, take a look at the Winchester 300WSM. It is more accurate (due to the shorter and fatter powder column) than the 300 Win Mag, it comes in a short action and it is ballistically equal to the 300 Win Mag. The 300 WSM is very quickly gaining popularity in the 30-caliber magnum class (most likely will eclipse the 300 Win Mag over time) and it has slightly less recoil. Another feature that is very positive with the 300WSM is that it is head-spaced on the shoulder. The 300 Win Mag is a belted magnum and is head-spaced on the belt which overall is a weaker design. I personally have shot over a half dozen elk with the 300WSM and can tell you it is an absolute lightning rod.
There you have it – my two cents
As far as gun dealers, I would take a ride to La Mesa and visit Finefirearms
http://gunssandiego.com/. They are also an SCH sponsor and have a knowledgeable staff too.
Also if you can – don’t scrimp on mounts and scope. They can make or break a hunt.
Good luck!
These are my express opinions derived from my experiences - I know less than most and half as much as some!