Like Tang has already mentioned, the answer to that will vary and can be subjective depending on your definition of effective.
My definiton is based on bullet velocity and the minimum opening and expanding velocity of the bullet. i.e., if I am shooting a 225 AB that has a mininum expanding velocity of 1800 fps, then where ever down range the bullet reaches that velocity is my max effective range for that load. Velocity will vary with rifle, load, elevation, etc.
As already stated, it all depends on the bullet chosen and the velocity it's achieving.
I run my 26" barrelled 338 with 225gr AB's at a velocity of 2900fps, it has an effective range of 800yrds with this combo, but it still depends on the size of the animal hunted as to whether this should be shortened.
This combo retains 1746fps and 1522ft/lbs @ 800yrds, adequate for most deer sized game, excluding Elk and Moose. Even though these figures are probably adequate for either, I wouldn't take the shot at that range.
I would limit myself to 600yrds on such game as the figures at that range are 2002fps and 2003ft/lbs.
It's all relative to what you're trying to achieve.
I want to exploit the high bc of the 338. I don't have a lot of money for a custom 338 edge or 338 lapua. I feel that the 338 wm would be a darn good long range hunitng rifle for anything in North America. I Don't know though. Mabye the 338 rum would be even better.
The 338 RUM would definitely be a better LR rifle than the WM. It will shoot a 250 bullet about 300 fps faster than a WM. It will also have greater recoil. The RUM is about equal to the Lapua and just behind the EDGE.
I have a 338 win mag light carry rifle with no brake. It is the largest 338 that can be shot effectively without a brake. If you don't use a brake then get the 338 winny. I shoot a 200 grain swift scirroco with .507 BC at near 3100 fps because of the recoil. My longest shot with the 338 winny was a 72" moose in Alaska at 1100 yards. That is extreme stretching it but with a spot shot and a good shooter it can happen. So that is what can be done with it. I think it is best with the 200 or 225 and is a great rifle.
Sako/Tikka T3 light. I have a Nikon Monarch 2.5x10 mil dot scope on it. Weighs about 7 1/2 pounds with scope and bipod. Shoots three shots touching at 100 yards. I like it and the same gun in 300 WSM for a light carry gun without a brake so I don't have to put ear plugs in before the shot. When stalking close range you just don't have time so I use these rifles when hunting in close. Either will get me out a long ways though if needed.
I have been giving the 338 win mag a new look. The upcoming .338 Berger VLDs are the reason.
I would think the 250 VLD would be the one to use. Many sources say that 2700 fps can be achieved from a 24" barrel. Even if this bullet could only get 2600 fps it would retain its energy very well. I think the higher projected BC of .762 (G1), .390 (G7) would change this chambering into another class of power/performance.
I realize this combo would require a short throated reamer and a long mag box to make it work. I took a 300 gr SMK and seated it to approx 3.8" OAL and it fit and fed just fine from another magnum with a wyatts box mag.
I do wonder what this bullet's low velocity expansion limits might be. Doing some basic number crunching, if it left the muzzle at 2600 fps with elk hunting conditions of 8000 ft/35 degrees/ etc
it would still be going 2219 fps or so at 600 yds with a bit over 2700 ft/lb of energy.
I realize this bullet is not available yet, but does anyone have any estimates on how well it might expand at lower velocities?
A 338 win mag weighing 7 1/2 lb with this bullet might be a great walk around elk rifle. Recoil would be tolerable with superior performance over the usual 250 gr bullets.
The 338 win mag often gets overlooked but it has that niche it fits perfectly into. Biggest 338 you can shoot well without a brake. It will take any game in North America at ranges beyond where most would ever shoot. I think it is best inside 700-800 yards and that is why I think the 200-225 grain bullets are best for it. They are much faster with a much flatter trajectory so you can use mil dots and quickly get on game without using clicks. You could certainly extend the range with a heavier high BC bullet but I don't think it is well suited for that. With a 250 grain bullet and a 7-8 pound rifle a brake is a must so you may as well go up to a bigger 338. The accuracy is as good as any 338 magnum out there and it would be a great shooter with the heavy high BC bullets.
On that Alaska hunt where I shot the 1100 yard moose I also shot several other critters. Big caribou bulls at 500 and 750 yards. A wolverine at 500 yards. Never missed a shot. Very fun rifle to shoot.