25-06 shoots a small bullet flat and fast which I used quite a bit. It was designed for shooting small to medium game animals at longer ranges and in this it is excellent. If most of your stalking is open ground hind and open hill stags then it is very good. Not a lot of recoil and point and shoot out to 250 / 300 yds, and at 250 it still hits hard. It is also perfect for long range foxing. In some respects the 25-06 mimics the flat shooting and ease of use of the 243 with an 80gn bullet, but with the 100 to 120 gn bullet it has that extra energy that does the job with much more authority.
270 is shooting 130 to 150 gn bullets and is the next step up - it is good all round flat shooting calibre, albeit with a bit more recoil and ideal for all deer and bigger animals. You could argue that for hinds it is a bit too big, with more energy and recoil than necessary and thus the 25-06 comes into its own.
Where the 25-06 is not so good IMHO is in the sub 100 yd shots on the body - the bullet is moving very fast and will cause a lot of meat damage and potentially not penetrate as well as a bigger slower bullet, or on smaller deer a 100gn from a 243.