Most efficient chamberings?

Maybe I just don't understand the question but this seems to be too subjective. A .25-06 is going to have a smaller barrel than a .338-06 so the rifle will weigh more, and the comparison becomes skewed. There are a lot of very effective means to reduce felt recoil. Mercury recoil reducers, pads, and best of all a proper fitting stock. Build what you want and if you think it's too much you can always lighten up on the powder or go with lighter bullets.

i think he what to build a rifle and is comparing possible choices to the 30-06 and is asking for other possible cartridges that he could look into. and having fun looking at efficiency as he defined it here. am i close?

For comparative recoil between equal-weight rifles, the deal is very simple: Add the weights of powder and bullet and multiply the sum by the muzzle velocity. Easy to see the percentage difference in recoil between two cartridges.

A common '06 loading is a 150-grain bullet at around 2,900 ft/sec, using around 50 or so grains of powder.

A common 7mm08 loading is a 140-grain bullet at around 2,800 ft/sec, using around 48 or so grains of powder.

The comparison-calculation is left as an exercise for the student.

We were just talking today of building a rifle around a box of free bullets. The rifle was a Mod 98 Mauser and the free box of bullets were .416 - 400gr. After a little research it looks like a .416-06 JDJ wouldn't present many problems and it should be able to be loaded to 2,200 fps without too many problems and loaded down below 1,100 for sub sonic pig hunting.

Usually, when I think of efficiency of a rifle-cartridge I think about powder burned to velocity (or performance). As was stated already, build what you perceive to be the best rifle and then take action to mitigate recoil if needed. However, an 06 is hard to beat in efficiency. Any of the 06 family are usually efficient.

Interesting question with a lot of variables. First of all, if I were you, I'd Deep Six the energy comparison. Bullet energy is a fine way to compare two very similar cartridges firing similar bullets, but to compare 2000 fpe from a 150 gr. 7mm bullet to 2000 fpe from a 210 gr. .338 bullet is...well...no comparison. Regardless of similar energies, the larger bullet will hands-down have the deepest penetration and be the superior disrupter of vital organs, hence the better killer.

Is the rifle you want to build just a shooting rifle or a hunting rifle? If it is a hunting rifle, what size game will you hunting? There's really no need for a .33, .35, or .36 caliber rifle if you'll only hunt deer.

Recoil takes on many forms due to many factors such as weight of the rifle and velocity of the bullet. A buddy of mine told me he'd much rather shoot a 338 Win Mag than a 300 Win Mag because of the difference in recoil, and I concur. On paper, the 338 should kick harder, but what causes the 300 to seem to kick harder is recoil velocity. That's what I consider "fast" recoil as in a the 300WSM and its 150 gr. bullet at 3300 fps. Kind slaps you unexpectedly whereas firearms firing heavily loads at lower velocities seem to have a slower, more heavy push.

Rifle weight. Years ago I built a 35 Whelen specifically for elk hunting. I had a 24" Douglas barrel put on it, and installed a banded type front sight and a receiver sight base in addition to the scope. So, the rifle is a tad on the heavy side. But recoil even with 225 gr. bullets approaching 2700 fps isn't bothersome to me. On the other hand, my Dad has a Remington 700 Classic in 35 Whelen. It has a thin 22" barrel, wears a fixed 4X Leupold and is very light. With the same load as I shoot in my Whelen the Classic seems to cause me to see stars every time I fire it. I worked up some loads for the rifle that rifle that ran a 250 gr. Speer a shade over 2500 fps. Brutal...

Stock shape. A couple of years ago Dad bought a CZ550 in 9.3x62. This rifle is of European design and the butt stock has lots of drop to facilitate use of the open sights.(Factor in recoil #1) Of course Pop mounted a scope on it, so when it's fired a fella has to sort of rest his jaw bone on the stock in order to see through the scope. (Factor in recoil #2) His handloads push a 286 gr at something like 2400 fps (Factor in recoil #3). Add these three factors together and the rifle is somewhat unpleasant to shoot. Drop the barreled action into a good ol' American designed stock with a nice straight butt stock with a decent recoil pad, and I'm sure it wouldn't be near as bad.

All that being said, I love both the 338-06 and the 35 Whelen. I have more experience with the Whelen but I've done quite a bit of load testing with Dad's 338-06 and 338-06 Ack. Imp. If you want to talk about efficiency, compare either of these with the 338 WM. The latest Hornady manual provides loads for the 338-06 that are only about 100 fps slower than the 338 WM. Nosler provides data, and loaded ammo for the Whelen that runs a 225 gr. at almost 2800 fps and a 250 gr. at 2550 fps.

If I had to pick only one, I guess it'd be the Whelen and for the sole reason that there's a HUGE variety of bullets available when you consider .358" pistol bullets which can be handloaded for nice light recoiling practice loads or for small game.

Good luck with your decision.
35W