I think that you need to consider cross-sectional density of the bullet. In this case, a 55gr 5.56mm projectile is close to optimum for that caliber. But a 150 grain 7.62 (.30 cal) has sub-optimal cross-sectional density, and therefore less effective penetration. Try comparing the 55gr 5.56mm round to a 165 gr 7.62mm NATO round, and you will see less of a difference for sure.
For the 15mm gun versus the 20mm - the 20mm is 25% greater caliber - that means more than 25% increase in bullet weight. The weights, shapes, ballistic coefficients, and cross-sectional densities of the bullets being fired from these cannon all contribute enormously to their comparative effectiveness - not just the muzzle velocities. A slower bullet with a much greater weight and optimum cross-sectional density will penetrate much farther than a lighter faster, less efficient bullet. For practical proof, look at the nature of hunting cartridges - medium and large bore hunting rifles, and long-range hunting cartridges. What do we know about the projectiles fired from these 15mm and 20mm cannons?