Which one would travel the farthest, project the most damage and strongest knocking-down power beyond 500 yards?
Well, they'll all travel
miles and take just about any 4-legged animal down at 500 yards. They also carry probably carry enough velocity and energy to take a 2-legged animal down at 2,000 yards if the shot was reasonably possible. So, for practical purposes based upon potential distance of travel and power, there is no difference. But, there are other issues to consider.
You mention a few factors that actually have inverse relationships. The more power, the lesser the trajectory, and vice versa. So the first issue is power. A general ranking of those in power @600y would give you about:
1.) 7mm Rem Mag.....2111ft/s.....1484ft/lbs
2.) .300 Win Mag......1948ft/s.....1516ft/lbs
3.) .338 Win Mag......1747ft/s.....1355ft/lbs
4.) .270 Win............1905ft/s.....1047ft/lbs
5.) .30-06 Spr..........1766ft/s.....1039ft/lbs
As you can see, if shot accurately, critters are no match for any of these, even at 600 yards. However, there are differences that could be discussed. The .300 Win Mag carries almost 50% more energy than the .30-06 or .270 and barely edges out the 7mm Rem Mag. However, the 7mm Rem Mag is easily the fastest at this distance by a fair margin. Additionally, the larger calibers (the .338 especially) probably loses more velocity and energy than the others at longer distances because it's such a larger, heavier bullet. One could conclude that the .338 Win Mag would have an advantage in power at CLOSER distances, but is disadvantaged, relative to the others, at longer distances.
Now, you can look at trajectories. Which of those require the least amount of holdover, adjustment, and have the least amount of drop at 600y? A general ranking...
1.) 7mm Rem Mag.....-47.10
2.) .270 Win............-54.88
3.) .300 Win Mag......-56.89
4.) .338 Win Mag......-65.56
5.) .30-06 Spr..........-66.40
As with power, you can also see that their trajectories aren't too far from each other, but with a clear advantage to the 7mm Rem Mag with the .270 and .300 very close in 2nd/3rd, and the .338 and .30-06 very close at 4th/5th.
One last thing to consider between these 5 loads is recoil. You'll find some fairly significant differences between them. In order of least recoil to most, out of about an 8-pound rifle:
1.) .270 Win............~17.00ft/lbs
2.) .30-06 Spr..........~19.00ft/lbs
3.) 7mm Rem Mag.....~21.00ft/lbs
4.) .300 Win Mag......~26.00ft/lbs
5.) .338 Win Mag......~35.00ft/lbs
If you're like me, you won't care how flat the trajectory is of the .338. With that much recoil, I simply won't shoot it as accurately as it can be shot.
NOTE: These are aggregate averages. This puts the .30-06 at a disadvantage because you can purchase a wide array of .30-06 loads... Light, Fast, and with good trajectories, or heavy, slow, more powerful, and with lesser trajectories. The other 4 do vary, but not by such a large margin.
So... In summary, all will get the job done, even well past 500y. However, for a highly skilled shooter with particularly difficult tasks, some have slight edges over the others.
