Can you compare the bushings in both chains and see if one is somehow different from the other? Looser, thinner, perhaps? This is a pretty dubious theory though, that would seriously screw up a drivetrain.

Do both chains mesh properly with the teeth? Perhaps the chainring is worn such that the old chain does not sit correctly within the teeth? This would take up more chain. Old chain with newer chainring?

Since the number of links is the same, and I assume the length being pretty close to the same even with wear, it must be the way the chain sits on the chainring and cog, somehow reducing the effective diameter of the circle.