Fellows with more experience will chip in here, but my experiences is this: I have a nice English side by side, and balance at the hinge pin suits it.
But, I have a single barrel trap gun (Ljutic), and I like some weight past the hinge pin. It makes my swing smoother to the target. IMHO these are two different types of gun with different handling characteristics.
Different strokes for different folks ... some people like their gun balanced at the hinge, some like the barrels lively and others shoot a gun that is barrel heavy. There are lots of weights available to change the dynamics of shotguns. You could experiment with lead shot contained in something, so it doesn't migrate inside the stock. Bill Malcolm
When shooting trap it is nice to have a gun with an adjustable balance system. This way you can set the gun for optimum performance depending on what station you are on. I move the balance point back for stations 1 and 5 and move it foward for stations 2, 3, and 4. HMB
Shooting trap requires a very deliberate or controlled, "quiet" gun movement. Quite different than skeet, sporting or, certainly, live bird hunting. Accordingly, different handling characteristics may be in order.
Senior Smoke is correct, it all depends how one holds their gun. If one holds the leading hand out towards the the front of the forend then the point of balance should be forward of the hinge pin. If one holds the leading hand towards the back end of the forend then the point of balance should be behind the hinge pin. Steve as far as the model 12 being the best balanced gun, it all depends on how one holds and mounts the gun. Maurice ( The Brit. )
Field guns will balance about 4.5" in front of the trigger. Most trap guns are around 5+/-", so they are a bit front heavy. If the weight is too far forward your usually well-co-ordinated trigger hand will have less influence and the butt will want to climb around on your shoulder
To me, balance is very important with my grouse/bird guns! Important because it's thrown to the shoulder and fired very quick at very fast birds.
Trap guns mounted long before a target is called for, doesn't need the English balance that game guns do. If I stuck my heavy trap gun to your shoulder and you tucked it in, I seriously doubt if you could tell me whether or not if that gun is balanced or not nor where it balances?
Carrying a game gun all day long can't be in the port arms position between the hands all the time. A lot of time is spent carrying it in one hand or other and if it's not somewhat balanced, it's a PITA to hunt with or carry for me.