I'm not qualified to completely explain it. However, I believe I know some of the factors that contribute to this phenomenon.
1) The larger diameter bullet has a greater surface area exposed to the pressure of the powder. Even though the .338 is only about 10% larger than the .30 caliber bullet, the surface area is around 27% more.
2) As you mentioned, most of the Edge's have longer barrels. Not only does this give the bullet longer to gain speed under pressure, it also makes a more efficient use of the powder charge (ie. more of the powder is burnt while the bullet is in the barrel).
3) Heavier bullets enable the use of slower powders, compounding the first 2 reasons above.
Compare the .308 winchester and the 338 federal. Same cartridge, except for the diameter of the projectile.
I'm sure that someone will point out any errors I've made in the above (I wouldn't be surprised if I've made at least one :confused: )
If some is good and more is better, then too much is just right.
My mind is a raging torrent, flooded with rivulets of thought, cascading into a waterfall of creative alternatives