I'll offer a little different take. If you have a good 30-06 you have the perfect back-up gun for almost every hunt. The 30-06 is always thought of as one of the top all around rifles ever. It does everything pretty darn well but isn't the fastest, flattest, or flashiest. Ammo can be bought at any place that sells ammo so if what you brought on a trip gets lost you are usually only out a trip to town and a few sight-in shots from being back in action.
I'd get whatever caliber you really want and keep the 30-06 for back-up. I always take a back-up rifle on hunts just in case. I mainly hunt big game with 2 rifles, a 264WM and a 300WM. I'm noticing a trend here and in other forums, most of the 2 rifle guys have something in the 25-06 thru 270 range, and a 300 or 338 magnum. It's pretty hard to beat that set-up if you want to use 2 guns. I know a lot of one rifle guys who have a 270, 30-06, or even more often now a 7mm Magnum. A lot of them use different loads for deer or antelope and elk.
I use the 264 with handloaded Berger 140gr bullets for most flat country hunts. Almost all my hunts for antlered whitetail, antelope, and sage country muleys I shoot that rifle. My 300WM is a custom gun for steeper country, mostly muleys and elk I shoot 180gr Accubonds from. It has a great pad and a brake and is very pleasant to shoot with them.
For normal ranges the ballistics are pretty similar so the holds are the same between them. Both start their bullets within 40fps of the same speed and both have pretty high BC values. Hornady's Ballistic Calculator shows the drop values within half an inch at 400yds. I have custom turrets on both with reticles that have the MOA markings for wind holds on longer shots. I try to range and dial for the range any time I can but if the shot is rushed or closer it's nice that both rifles have similar ballistics. If there is time I'll check the wind too and hold for that. I try to get close though, most of my game has been taken inside 300yds.
Honestly most of us think about this to much. Almost all my game could have been taken with a 3-9x scope and a 30-06. A few I was glad to have the set-ups I did instead but not many. We should probably all have one good rifle that would cover deer, antelope, and elk plus a cheaper Ruger American type rifle in the same caliber with a decent scope for back-up. Then we should get Ruger American Rimfire 22 rifles and put on a similar scope, and practice field shots with a few thousand rounds each year. It's more fun to have more rifles though.