In my view, a 'good balance' means a gun mounts evenly and smoothly.
When not balanced well, either the barrels tend to rise first, or the stock, both needing small but concious correction.

But it is more complex than that because guns that feel best usually have a centralised weight concentration and so a lower moment of inertia. This is achieved by hollowing in the stock and careful striking up of the barrels to give thinner walls near the muzzles (where the pressure is low). This is why some 'best' British guns often have (and have had from new) quite low wall thickness towards the muzzles.