For most people, I would say the 25-06. To compare these 2 rounds we should logicaly look at what each cartridge offers over the other.
25-06 advantages
Common brass & much cheaper with more firings per case.
Less powder
Bullets are a little cheaper
Overall quite a bit cheaper to reload
Much cheaper factory ammo
If you decide to shoot Varmits it is much better for that.
Less recoil
Less blast
Easier to work up an accurate load, but both rounds can be VERY accurate.
Easier to resell, although most people with a good 25-06 won't sell theirs!
Better barrel life, but this is overblown by many.
264WM advantages
More killing power, but for Deer it is a mute point as both rounds have more than enough power with the right bullets & loads out to 400 yards.
For Heavier bullets if you decide later to hunt Elk or bigger animals the 264
is better for these animals.
The heavier bullets in the 264 will have higher sect. Densities, but again
a mute point for Whitetail. I have never been able to stop the 25cal. 120 Nos. Part. or the 115TSX 25 cal. in any Deer at any angle.
The heavier bullets in yhe 264 have a higher BC which offers better long range possibilities, but only at longer ranges & it would take quite a distance before it matters. I have a tuned Sendero in 25-06AI that is a pure death ray on Deer & it does what I want in spades.
So what it boils down to is that if you use the right bullets & loads for
Whitetails, your stated purpose, the 25-06 will serve you well out to 400 yards. The only way that the 264 will give you something extra for Whitetails only is IF you want a specialized "bean field" type rifle & want
to set it up for longer yardages than 400 yards. Only a select few acquire the tools, well tuned rifle, best ammo, optics, & practice with wind doping
skills & restraint. Only you can determine if you are one of those few &
no one on this site can tell you, me or anyone else if we should be of this slim minority. And please let's don't go there, my answer is only to point out the abilities of the cartridge, because it was asked & not to point out what any one person should do with it!!!