I have heard of very few people who regretted moving up to one of the 30 cal magnums. They represent possibly the finest all around caliber and cartridges for hunting any NA big game, save maybe the biggest of the bears, and they also work pretty good on these too. I have used 4 of the big 30s over the years to harvest 100s of big game animals on several continents and can tell you that I have never wished I had a larger gun, nor can I say, with a couple exceptions, that I wished I had a smaller gun. I have taken game from 10 lbs to more than 2000 lbs with 300 mags. It just works !!!
The recoil is manageable in a 7-8 lb rifle which carries nice all day, and "reaching out to touch something" at 500 mtrs is a no brainer on a calm day with a good rest. What I can also say though, is that if you never shoot at game beyond 200 mtrs and this is the maximum of your shooting comfort zone, you will likely see very little difference from your '06, given the same impact point, on ungulates. I like to go afield with all my bases covered whether it's a medium sized grizzly at spitting distance or a good ram at 5-600 mtrs or anything in between, and there are very few cartridges that cover this style of hunting.......the 300 magnums make up most of the cartridges in this category, and the 300 Win is right near the top of the list.
Just for the sake of trivia, I own and shoot a 300 WSM, 300 H&H, 308 Norma, 300 Win, 2 or 3 X 300 Wbys and a 300 RUM, and I just bought, but don't have in my hands yet, a Rem model 7 stainless synthetic in 300 SAUM.........the only two I have not taken game with are the 308 NM and the 300 H&H, both of which are relatively new to me. You might say I'm a bit of a 300 fan..........incidentally I have a couple '06s too, but as I recall, I only ever shot one moose with an '06.
I have always said I am a much better shot than a tracker so I like game to be laying right where they were standing before the loud bang, and the 300 magnums seem to do this very, very well and on game they are not likely to handle in this way, I usually use a 375 H&H to the same effect, or the "ultimate one rifle hunter cartridge" ........THE 340 WEATHERBY MAGNUM !!!!!!!