Flyingcircusboy,
You asked "Which one has the best overall characteristics as far as trajectory, muzzle velocity and "knockdown power"
The 338 has the most knock down power, by virtue of much heavier bullet weights and greater frontal area of the bullets. But the 300 RUM has the higher muzzle velocity and the flatter trajectory.
My reccomendation for a rifle for the serious elk hunter would be the 338, my vote goes to the 300 Win or possibly the 300 WSM for a regular deer hunter who would like to be ready for an occasional oportunity to hunt larger game.
While the larger magnums do give higher performance levels, their larger case capacities require much larger doses of powder and subject the shooter to much greater recoil force.
Many magazine articles have been written about the law of diminishing returns, and many more pages devoted to explanations of felt recoil. Most experts find the average shooter can not learn to be comfortable with more recoil than that which is produced by the 30-06. I personally find that I can only comfortably fire twenty to thirty rounds from a 300 Win Mag or my 7 MM STW in a single session at the bench. After that fatigue sets in and shooting becomes painful. Continuing beyond that point would quickly lead to an induced flinch, NO THANKS. And I use a PAST recoil shield and Pachmeyer Decelerator 1 inch recoil pad on the rifle.
I would buy the 300 Win in the Win Mod 70 Classic. I have owned several Win 70's in 30-06, 300 Win Mag, and my favorite, 264 Win Mag. With a single exception, I have been able to make all of them shoot less than MOA with simple tuning, glass bedding, and load developement; all done at home. And I find the Mod 70 a good looking rifle. It can be obtained in many combinations of blued steel or stainless with synthetic, walnut, or laminated wood stocks. Walmart is now carring a new style of Win model 70 with a synthetic stock in 300 WSM for a very reasonable price. It is not as pretty as the Mod 70 Classic in walnut, but the price sure is right.
I just find that the minimal performance gains to be had in the 300 Dakota, 300 Pegasus, 300 Kong, 30-378 Wea, 7.82 Warbird, 300 RUM, Or even the 300 Wea Mag just cost far to much in terms of recoil, powder consumption, and ammunition cost.
You mentioned that you do not intend to handload ammo for you rifle. Another benifit of the 300 Win Mag is ammo availability, almost any place that sells ammo will carry 30-30, 308, 30-06, and 300 Win Mag. Decent ammo is usually priced right too.