Since I have both:
The two are so close in practice as to be practically identical.
Except:
The velocity that can be achieved does depend to a large extent on the action. For example, a 6mm Remington that is perfectly safe in a Remington Model 700 action is way over pressure in a Remington Model 788 (think perforated primers and sticking bolts). I found this out working through some of Ken Water's 6 mm "Pet Loads" (Note to the unwary: If Ken said it was MAXIMUM, I suggest that you stay well away from it).
How efficient the cartridges are is, in part, a function of case volume. A 243 has a smaller volume than a 6 mm Remington. With the same action, bullet, primer, and powder, the 243 can achieve the same working pressure as a 6mm Remington with less powder. Working pressure is one of the factors translates to velocity. BUT:
Some barrels are faster than others, and all chambers are different. (I know of two 270s that are "identical", except that one chronographs about 200 fps faster than the other WITH THE SAME LOAD).
So, we are essentially discussing something akin to how many angels can dance on the head of a pin.
Your Mileage may vary.
A final note to new handloaders that want to become old handloaders: Pay very close attention to the powder burn rate and adhere to the published data. Only put one type of powder on the bench at one time and triple check that you are using the correct type. Note that some pistol powders have labels very similar to labels on rifle powders. Just because the powder will fit in the case does not mean it is safe. If you find a load that is safe with, say, 50 grains of 4831, take it on faith that if you stuff 50 grains of, say Red Dot in the case, you have just created a very dangerous bomb that will destroy the firearm and who ever is shooting it.