I use the 7mm rem magto harvest antelope, wt/mule deer, elk and moose with no problems. Like mentioned I'd feel comfortable tackling anything but the big bears withmy 7mm rem mag. Recoil is not bad and ammo selection/cost is very good for anything upto moose sized game for NA. With todays choices in bullets one can really make a cartridge serve multiple purposes if desired. I took a bull elk and bull moose this fall using 140 gr TSX and the performance I received was outstanding. 2-1-shot kills with a grand total ofless than75 yards covered by both animals after the shot, great penetration/tissue damageand hardly any meat damage thanks to the construction of the Barnes bullet.

I previously owned both a 300 wm and wby, I see really no practical difference between these and my 7 mag for what I hunt currently. I also owned a 3006 and while it also proved to be a good cart. the 7mm does just enough different for me to prefer it over the 06'. The only one you mention that I really like is the 338wm but only for the bigger game. I have never owned one but have shot them. Right now I don't have the tolerance due to shoulder operations to allow me to handle a full fair weather day at the range, otherwise I would have one myself. But if your looking for a rifle that will be for the sole purpose of hunting elk, moose and possibly the big bears the 338wm is a great option to have in your cabinet. I really don't consider it a all arounder though, a little large for deer or antelope.

If your looking for an all arounder, one rifle doesmost the 06', 300wm or 7mm rem mag will work well, really splitting hairs. Either could be used in a pinch for a grizzly hunt, the 300wm would be the better of the 3 in this scenerio but still not ideal IMHO. However if you have a smaller game rifle that you enjoy/like/feel confident in for your deer sized huntsbut really want a bigger game rifle, take the plunge up to the 338wm. Not a speed demon but packs a great punch. The recoil is higher than a 300wm, but seeing you don't find it excessive I think you'll have no troubles handling the 338wm.

Best of luck