Between calibers it's more useful to compare bullets of similar sectional density than bullets of similar weight. On that basis the smaller one normally shoots a little faster (If they're both essentially neck diameter variations of the same cartridge).
Why would you want "hard" bullets? Ungulates clued in to trauma plates in your neck of the woods?
While comparing sectional density is a good idea, there are many other factors to consider when thinking about suitability for game animals. It is true that smaller calibers with a specific SD will often shoot "a little faster" than larger calibers with the same SD from any specific case, but no one would ever argue that a 140 grain .27 cal bullet from a .270 (SD .261 and top velocity in Nosler #5 3018fps) is less effective on moose than a 120 grain .25 cal (SD .260 and top velocity in Nosler #5 3090fps), even though it is going a little slower.
That difference in velocity is less than the differences between rounds of a specific reloaded lot of one caliber. The heavier bullet (momentum) and larger diameter (wound channel) are also factors. It is also true that with a .270 you can shoot 160 grain Noslers with a SD of .298. No .25-06 can do that. There is much more to hunting effectiveness than velocity.
As for "hard" bullets, I used that slang to mean premium bullets that will not fragment on impact like the Nosler Partition as opposed to say the Ballistic Tip. I should have been more precise.
I believe the smaller the caliber in relation to game size, the more important it is that the bullet hold its mass to provide as much penetration as possible. On game animals the size of moose, penetration becomes an important factor.
I know no one who considers the .25-06 as equal to the .270 as a moose round. I actually see the .270 as a kind of "minimum" moose round and prefer larger diameter bullets, with better sectional density than either of those rounds, and at similar velocities, as much better for moose. I use a .300 Win. with 200 grain bullets for moose (SD .301 and velocity at 12 feet of 2940 fps)
So a .25-06 will absolutely kill a moose if the hunter understands its limitations. It is not, however, my idea of a good moose round.