Railgun caliber, power, and capacitor limits

Can a small railgun projectile outperform a much larger conventional shell?

Potentially, but the decisive limits are power generation and capacitor storage rather than caliber alone.

A small, long projectile can strike with great energy, so caliber alone does not determine railgun effect. Raising performance rapidly increases generation and storage requirements. A nuclear reactor might supply sustained power, but the weapon still needs compact capacitors able to charge and discharge at the required rate. Shipboard layout and energy management therefore become part of gunnery design. The answer makes electrical infrastructure, not projectile diameter, the controlling constraint.