Well,, I have owned one 25-06 for now approaching 40 years. And its being rebarreled into a 280 AI. I have another 25-06 that I have owned only 8 months. And its going to be re barreled to something more useful.....
Here's the problem with the 25-06: It is and was conceived to be a "one gun" solution for varmints to deer. That means compromise. The twist was set slow, as varmint slugs did not need a fast twist. And the "heavy" slugs in the 120 gr range had to deal with the consequences. And forget anything over 120. And heavy lead core .257 bullets are NOT available.
In the end, the 25-06 is too much for varmints, not quite right for deer (but does both well enough, if you really want to have one gun only).
Back when long distances were 300 yards and people wanted maximum velocity so they did not have to worry about hold over, never mind having a scope with turrets etc, super fast cartridges were the best solution to get to say 300 or 350 yards. The 25-06 can do that.
But its not an accuracy round, horribly over-bore and with the slow twist, a pain to stabilize even the mediocre BC slugs that are out there.
I would never, ever recommend a 25-06 as a deer round. For those posters that say its a "bang-flop" deer round. Well you have not shot enough deer with one. Moreover, many of my 25-06 kills through the years, though SPECTACULAR BANG-FLOPS, were the result of a bullet that just plain blew up. And the process of dressing out the animal and salvaging the meat (a part I consider my ethical duty) was a royal pain.....
NOW -- to my recommendation. If you are deciding between 25-06 and a 6.5 Creedmoor, then you have not researched your options enough. First decide your action. You want short action? You need to consider CM or 260 or 260 AI if you hand load, Maybe 6.5-284 if you don't want to shoot heavy bullets long range. You willing to stay long action? Then the world is your playpen. LOTS of cool options in very high BC bullets. 6.5-06, 6.5 Sherman, 6.5-285, all the 6.5 Magnums, 270 and 270 AI, and in 7mm you can do 7mm RM or 280 AI.
Personally, I am also having trouble deciding. But one bit of advice: the 25-06 is not your ticket to joy...