The 7mm-08 will outperform a 7x57, every time. This is due to the 7mm-08 being a more modern cartridge, thus loaded to a higher average pressure then the 7x57. SAAMI calls for the 7mm-08@61,000PSI while the 7x57 is only at 51,000PSI. The 7mm-08 will be faster with all bullets, Hodgdon shows the 7mm-08 with 160s averaging about 2650fps from several suitable powders. The 7x57 is only at 2500 with a 160, and that's with only about 2 powders. Most were significantly less. In addition, the 7mm-08 has a much better reputation for accuracy, being used quite a bit in various disciplines. The 7x57 generally has a reputation for attaining satisfactory field accuracy at best. The 7mm-08 is a true short action cartridge at 2.80", where as the 7x57 is not a short at 3.071", but really isn't a long action round either. It is just long enough to not work well in most short actions, due to limiting COAL greatly or not fitting at all, but a long action is much more than is needed. Most cartridge discussions are based on subjective feeling, but to me, this is one of the objective ones with a clear winner. The 7mm-08 Rem.
I think you are a paper comparer with no practical experience with regards to the field performance of the 7x57mm. The 7x57mm has one of the best track records in Africa as a light rifle. 7x57mm are not built on short action but rather on medium or intermediate actions.
Developed in 1892 it has a great track record. Although as stated SAAMI pressure is at 51000 psi C.I.P is at 56565 psi. These pressures are for factory ammo. In modern actions, you can load the 7x57mm to exceed anything you can do with a 7mm-08 in any bullet weight.
Typical 7x57mm have a rifle twist of 1:8.66" specifically to stabilize heavier bullets. Heavier bullets are much better for use on African game than light for caliber bullets.
The 7mm-08 has a rifle twist of 1:9.5" which is better for lighter bullets. If you have a 7mm-08 that will shoot the heavy weights accurately, that is great. If not you will be further limited to the game taking capability.
The all american need for speed is obvious. Although the 7mm-08 is a great cartridge the 7x57mm always has been and still will be the better choice for African plains game. Especially when including the larger plains game species.
Is either the 7mm-08 or the 7x57mm the ideal cartridge for Eland? Most certainly not, especially for a visiting client it is marginal. In an experienced african hunters hands it would get the job done.
Paper punching sub MOA groups, light bullets and high velocities and chamber pressures are not needed for African PG.
The 7x57mm loaded with a premium grade 170-175 grain bullet will kill all the plains game in Africa(yes it is marginal for Eland), as it has done for 126 years and will continue doing so.
I would still not recommend either to a client for use on a trophy sized Eland bull, unless I have hunted with the client before and know his abilities. Unfortunately Eland are not easy to hunt, once wounded or spooked they just keep going. Rather use a more appropriate caliber.