I'm sure I could have killed both those red deer with my 30-06,but in my case for the 338-06,I had a 30-06 rifle that I was going to rebore or rebarrel.I tell you,most people don't realize just how good a 30-06 is especially if you reload for it,it probably is right up with some of the 300 magnum factory rounds and what it does give up to them probably blows out the exit side anyway.I worked up some 200gr loads for my 30-06 and they ran 2650fps.I also did some for my 300 Win Mag and they were 2860fps.I have several loads for my 338-06 that are right there with the 300 Win Mag with the 200gr Accubond.Here they are
61.5grs R-17 2830fps
59.5grs BLC-2 2830fps
56.0grs Varget 2849fps
59.0grs Big Game 2812fps
59.0grs CFE-223 2807fps.

And when you have a 338cal bullet going the same speed as a 30cal bullet of the same kind,which on do you think will have the bigger whoomp when it hits?

~Molɔ̀ːn Labé Skýla~
As Bob Hagel would say"You should not use a rifle that will kill an animal when everything goes right; you should use one that will do the job when everything goes wrong."Good words of wisdom...............