I would choose 300 wsm in a browning just for the little longer barrel. 300 wsm, is diffently more effecint over 300 mag.

someone told me. that the 7mm mag has more of a bite than the 300win mag, is that true?

Quilly - I'm the most recoil-sensitive guy you'll come across (shoulder surgeries), and I can shoot all the "standard" 7mm mags up to the Weatherby number and show no ill effects. The only .300 mag I can handle is the WSM (and probably the SAUM, although I've never shot one).

Good Dogwork and Good Hunting

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As stated earlier either is fine.
The 7 mag will have slightly less recoil, if you are recoil sensitive it has a pretty good kick, and if you don't like it you will hate the 300 win.
If you are recoil sensitive go with the .280 or 30-06 the animals won't know the difference until the range gets well past 200 yards.
If you are OK with recoil toss a coin, either is an excellent caliber.
My personal preference is the .300 Win with 200gr Partitions for elk.
I had a mercury recoil suppressor installed in the stock which greatly reduced the recoil.

Looks like some guys are starting to compare recoil in some cartridges. If you're curious about the recoil check this web page http://www.chuckhawks.com/recoil_table.htm. It'll give you a good idea on the different cartridges.