The 338 Federal with a 225 gr bullet at 2450 fps will have a muzzle energy of approx 3000 ft-lbs, while your 300 Win Mag and a 220 gr bullet at 2650 fps will have approx 3430 ft-lbs of
muzzle energy. (using the velocities you have given)
So the 300 Win Mag wins the muzzle energy race. This is due to the higher initial velocity. If initial velocities were equal, the 338 would have more energy, but only by 100 ft-lbs.
The 338 225 gr bullet has an SD (sectional density) of 0.281 and the 30 cal 220 gr bullet has a SD of 0.331 The higher the SD, the better the penetration is.
So the 300 wins the penetration competition. And this is before you have added the extra velocity of the 300 Win Mag. While SD may be an indicator in a bullets ability to penetrate, it alone does not guarantee "stopping power".
If you were to compare the same type of bullet (i.e. Nosler Partition), the 338 225 gr bullet has a higher BC (ballistic coefficient) than the 308 220 gr bullet vs (0.454 vs 0.351) which means a higher degree of aerodynamic efficiency which will retain its velocity better over range. At a certain point down range the 338 bullet will eventualy carry more energy than the 308 cal bullet.
The 338 cal bullet has a larger frontal area than the 308 cal bullet (due to larger diameter), which will impart more energy on the target with the initial impact and penetration, than the 308 cal bullet. Some would argue that it is marginal, while others will argue that it is distinct. It may not be as readily apparent in this instance vs a larger difference in bullet diameters as in a 6.5 cal bullet and a 375 cal bullet.
So, it would depend at what range you are considering the stopping power to be measured at.
Are you considering this for on-game harvesting performance and killing power or for stopping a charge at short range?
I can say from experience that both cartridges are effectiveon big game in the field from caribou to bison.
Each has its strengths and advantages. It would depend on what you are hunting, and in what type of terrain or environment.
Sorry, it was late whenI posted this, and missed an important bit:
The old rule of thumb recommended by many experienced riflemen, guides and PH's was:
You want a minimum of the following remaining energy's, at the animal, for the following classes of big game in north america, for aduequate penetration and killing power:
1000 ft-lbs on deer sized game (also includes, black bears, antelope, sheep, goats and caribou)
1500 ft-lbs on moose
2000 ft-lbs on elk, bison and big bears (grizzly, brown and polar)
For reliable penetration to the vitals, through bone and tissue from various angles, with the above remaining energy, for north american game, the recommended SD of the bullet was 0.250, and on Agrican dangerous game, the SD was 0.300