While I'm not sure that an answer such as "it is all fear based" is technical...
The 338 federal is a short action cartridge (thee 308 Win necked up to 338 cal) that provides plenty of performance for big game such as moose, elk and larger bears in a short, handy rifle, for those who like to hunt and get closerto their game. The 210 gr bullet starts at 2630 fps and carries almost 1900 ft lbs of energy at 300 yards, where it is still moving at 2000 fps.
The 338 Win Mag is a great cartridge that requires a long action rifle with a magnum bolt face. (As data was supplied earlier, I will not repeat here). Rifles tend to be longer and heavier; a good thing due to the increased amount if recoil. It is ideal for elk, large moose, bison and large bears (although some may argue that the big brown bears should be dealt with with bigger cartridges such asa the 375's) at longer ranges than the 338 Federal, as it is carrying more energy due to heavier bullets usually used (225-250 gr) started at higher velocities.
The 338 Lapua is based off of a much larger cartridge case and requires the larger magnum actions (375H&H), making for a heavier rifle. This cartridge was originally designed to be a long range sniper cartridge with reduced recoil to the huge 50 BMG, which made for lighter rifles for battlefield conditions that would also provide better accuracy potential at long range due to the reduced recoil.
While I own, have owned, or have used all of these cartridges (plus the 338-06) from the bench and in the field on game, on game from caribou, elk, moose, grizzly bear and bison, I can tell you that they are all effective.
Obviously, the Federal is the most pleasant to shoot,due to the smaller powder charge, but don't let this deter you from this efficient cartridge; it performs a lot better than its' paper ballistics may indicate.
WItha 180 gr bullet, it will outperform the grand old 30-06 with the same bullet weight. And out to 300 yards, will privide all the energy needed for the game listed above.
The 338 Win Mag isa great cartridge, but is above the recoil tolerance level of the average guy. If you can handle it well, it is a rifle that can do every animal in north america well.
The Lapua definitely has a significant level of recoil, but is manageable, if you are used to this level of recoil. A friend had a lightweight hunting rifle built on a Model 70 action, that shot very well, and when using itin the field, I did not find it to be too much,but definitely more than my own 338 Win Mag. It definitely performs with the heavier bullet weights (above 250 gr) better than the Win Mag. Most rifles produced in this cartridge are definitely bigger, longer and heavier, and may not be the best hunting rifle choices. It is definitely more expensive to shoot! Handloading helps, but is still not as economical as the Win Mag or Federal.