More details from my earlier post.
For your stated purpose any of the 3 are adequate. A 270, or even 280 loaded with modern 150-160 gr bullets will do anything a 30-06 will do with 180 gr bullets. A little on the light side for 1200 lb brown bear, but adequate for anything else in North America.
The 30-06 gives the option of 200-230 gr bullets which moves it into another category. Most people never consider the heavies, but a 200-230 gr 30 caliber bullet will do anything a 225-250 gr bullet from a 35 Whelen will do at ranges up to 150 yards. Beyond 150 yards the 30-06 easily outclasses the 35 Whelen. 35 Whelen recoil is exactly the same as 300 WM. Start shooting those heavy 30's at 300 WM speeds and it isn't even close. If I'm getting 30+ ft lbs of recoil anyway it might as well be from a 300. Which is exactly why I sold both my 35 Whelen and 338-06.
When the Whelen was introduced in 1922, (and with the bullet technology of the day), it offered some advantages over 30-06. In 2016 it offers zero advantages, and several disadvantages. Aside from its lack of moderate to long range performance, it doesn't perform any better up close, even on big stuff. There have been multiple tests and studies done on larger African or Alaskan game and in every example the heavy 30 caliber loads out penetrated everything up to 375 magnum. If someone is looking for more performance than 30-06 or 300 magnum, the 375 is the next step up. There is nothing in between that offers any real advantage.
Recoil is always a factor:
A 270 will have the least, somewhere in the 17-20 ft lb range depending on the individual rifle and load. A 30-06 will be in the 18-22 ft lb range. A 35 Whelen loaded with 225-250 gr bullets has exactly the same recoil as a 300 WM loaded with 180-200's, about 30-33 ft lbs recoil. The 375 mags are in the 38-43 ft lb range.
I've owned most all of them. When you factor in everything including recoil and look at the option of having a lighter weight more portable rifle I keep coming back to the 30-06 as the best balance.