Burn timing, charge condition, and breech obturation

Can a shorter gun with a faster-burning charge match a longer gun with a slower burn?

No: the longer gun's slower burn gives greater range and accuracy in this comparison, while charge consistency, projectile weight, rifling, and gas sealing also affect performance.

In this comparison, a longer gun with a slower-burning charge gives greater range and accuracy than a shorter gun using a faster burn. Modern cartridge manufacture permits closer control of the burn so that useful gas expansion continues until the projectile leaves the muzzle. In older bag guns, the charge must suit the projectile's weight and the gun, while rifling twist is another part of the relationship. Stable temperature and protection from damp help keep bag charges consistent. A brass case can expand to seal the chamber against escaping gas; a bag gun instead needs a breech mechanism that supplies the necessary obturation.