The .318, if loaded to the same pressure as the '06- nominally 60,000psi (SAAMI-pezio), will produce greater velocities with the same weight bullets. It does very well at make 2,400fps (probably 28" bl.) with it's much lower standard working pressure of 48,000psi (pezio).
Note a 250gr. .330" bullet is considerably shorter than a 250gr. .308. I suspect Sectional Density of the 220gr. .308 might be quite similar or equal to the 250gr. .330".

Both ctg.s will usually make 2,400fpsd with their respective long bullets. Although Barnes used to make a 250gr. .308" bullet, I've read the standard 10" twist was not capable of giving it good stable accuracy. I have not tried them in any .308 cal. rifle.

http://kwk.us/pressures.html

The .318 has grater capacity than a .30/06. To match it, you would need an Acley Imp '06- or close.

The .441" shoulder of the .30/06 is sub-par - as-is, it's .308" bullet compared to a .330" bullet. The '06 has a 17degree 16minute shoulder compared to a .451" shoulder with 62.24 degree shoulder angle. Yes - the .318 is 1/10" shorter in case length, but more than makes up for it in shoulder shortness (longer body) and larger diameter shoulder as well as shorter neck.

According to JJ Donnelly, the '06 capacity is 68gr. which I think is high as he lists the same capacity for the improved 06 cases. 63.5gr.is much closer to the actual truth for the '06.

The .318 Rimless NE is listed as 68.72gr., which is quite close to the actual, considering the shoulder is listed as .451"