Charles_E has a very good approximation for the recoil of the 6.5-284. My 6.5-284 weighs about 14-pounds, with the Leupold 8.5-25X mounted. With 142gr. A-Max or MatchKings, the felt recoil is almost identical to my old .30-06 Palma Match rifle (with 155gr. bullets). The 6.5-284 bullets are moving along at 3,000fps, the 06 moves the Palma bullet at about 2,850. The recoil isn't remotely as bad as my .30-338 (which is almost exactly the same as your 300 Win Mag), but if you are planning to shoot a whole match with the 6.5-284, with a bunch of sighters, your shoulder will definitely bother you at the end of the match.
Do not despair. The same gunsmith who built my 6.5-284 also made one for himself... a much better one from the recoil perspective. Instead of a Remington 40-XB prone-stock, like I am using, he used a thumb-hole that looks like an H-S Precision tactical stock. Along with the high-comb straight-line recoil reduction of the stock (with a nice KickEez pad), he also installed a Vias muzzle break. I would approximate the felt-recoil of his gun to be approximately what I feel when I shoot an 80gr. bullet out of my 243. In short, he tamed it beautifully. If you are intent on pursuing the 6.5-284, you might want to consider the thumb-hole stock and the muzzle break.