Let me state up front that I have no experience with either round, thus my suggestion is less qualified to your direct question. Consider this though. You stated whitetails as the target animal and the std 270 has been a proven performer at the 400yd distance for many years, however, the 300WM will always do it with more authority.
The kicker you through in was enjoyable shooting, to that I can answer easily. No matter which caliber you invest in, also invest in a top level recoil pad. i can tell you that from many years of shooting, that a top quality pad will tame rounds well below what the factory sticks on there. What a HUGE difference in my '06 with the Kick Eze pad installed. In addition, I needed to bring my eye up some to properly align it with the scope, and still maintain a solid cheek weld. i did this with a Kick Eze cheek rest pad. Those two things, make my 30-06 as pleasant to shoot as my 243 with the factory pad, I am not exaggerating one bit.
I am sure any of the top brands of recoil pads will give similar performance, but do not overlook this detail when putting the gun together for your dad. I will be 60 next birthday, and have shot rifles since I was 8 yrs old. Recoil gets less fun and more noticeable, as you get older.
As an old fart myself, given your criteria, I'd suggest the 270, with a good scope and pad, and no regrets.
Now if you ever think you might go after heavier game, the 300 WSM loaded with the Barnes 130gr TTSX, would shoot like a laser beam, and similar recoil to the 270.
I forgot to add, theses would be for the deer, leaving heavier bullets available for the bigger critters. if only deer, go 270. My unqualified opinion.