In the 25-06, it's the 115-120 grain bullets that separate it from the 6mms and afford it much more authority on the business end.
For deer? The good ol' Sierra 117 grain Pro Hunter, a flat-based spitzer, is one of my favorites for the cartridge and will give you around 3000 fps from a 24-26" barrel when driven by 50 grains of Re-22. That load has proven to be extremely accurate in a number of 25-06 rifles.
If you want a sleek, flat-flying bullet, the 115 grain Ballistic Tip is a top prospect, but don't overlook the game-taking capability of the time-proven Partition, either.