A overbore cartridge need a longer barrel to perform at max.
7-08 and 308 often use a 20 inch barrel but 7-08 might be better of with a 22-24 inch.

John and Savage are correct, of course. Another key is your use of the term "bullets of the same weight". .308 bullets of the same weight as .284 bullets have less sectional density than the .284's. this means they have less bearing surface, hence less friction, plus they have both lower inertia and a greater base area for the propellant gases to push on.



Now, if you said "bullets of equal sectional density" rather than weight, I think you'd find that both cartridges would produce similar or identical velocities, albeit with DIFFERENT powder burning rates! Look at your example: The 165-grain .308 bullet has a sectional density of .248. A .284" bullet of that SD weighs 140 grains. I can fire a 140-grain bullet out of a 7mm/'08 just as fast as a 165-grain bullet from a .308! And both will perform pretty much the same flying downrange, and on the target, provided they are of the same shape and construction.



Does this explanation clarify matters a little?