Six of one...

Half-dozen of the other!

For those who think that the WSM are somehow inherently inaccurate by design, then tell me why ALL competitive benchrest cartridges follow they same general design as the WSM cartridges (i.e. short, fat non-belted case with nearly straight walls and a steep shoulder angle). Personally, all else being equal, the WSM are as accurate or slightly more accurate than their long-action belted cousins. I had a Tikka T3 Lite in .300WSM that was an honest-to-God sub-MOA (but not by much) rifle with handloads when bagged in on the bench. It was a fine shooting rifle, but I didn't like how the 6.5lbs rifle beat the snot out of me every time I shot it. I shortly realized that it was starting to give me a flinch and so I got rid of it.

I, personally, believe that these "reports" by "experts" that the WSM's are inaccurate are likely projecting their poor shooting of a hard-kicking cartridge onto the cartridge itself rather than placing the blame on themselves where it belongs. The fact is that most shooters just can't tolerate the recoil and muzzleblast produced by the short -barrelled (for a magnum) ultra-light short action rifles that the WSM's are commonly chambered in and still shoot well. I've been-there-done-that-got-the-t-shirt. It's been my experience that most men are just too darn proud to admit that they can't tolerate the recoil so they blame the gun and not the flinching egotist behind the trigger.

I know you asked about the .300WSM v. the .300 WinMag. And if it were me I'd pick the WinMag if buying factory ammo or the WSM if handloading. I'd bet that that the BAR will shoot just fine with either. However, unless you are genuinely one of the select few that can shoot a magnumb well, I'd recommend that you consider the .30-06 or .308Win. Plenty of power for just about every hunting situation in North America (except dangerous game), plenty of reach for almost all realistic hunting ranges, ammo is relatively inexpensive and available everywhere, and it won't loosen your teeth every time you pull the trigger especially in a semi-auto.

Good luck with whatever you choose.

Mike