Adam, that's a great 2:00 a.m. question, and one to ponder when you can't sleep. I'm sure you'll get lots of answers here that are thoughtful and based on lots of experience.
Obviously the gun that you have confidence in is the one that has the "best" balance, but what's the fun in using only one gun?! Here are my thoughts on my own shooting experience (which is exclusively at game birds -- my Forum friends who shoot clays will have very strong and knowledgeable opinions based on
lots of shooting).
For game like grouse and woodcock I can shoot a rear-weighted gun as well as any. The shots are quick and seldom do I get the chance for long crossing shots. This kind of weight balance is great for helicoptering woodcock in very tight cover.
For birds in more open cover where I can be a bit more deliberate, I like the weight between my hands...or slightly weight forward. For the wild quail we most often hunt, longer barrels and weight stability works best for me. Shots are quick, but more deliberate. (For wild Bobs in the timber, I recommend leaving the gun home and just watching.
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For birds like dove and ducks that I can generally be more deliberate about, I shoot a weight-forward gun as well as any, especially on longer crossing shots (which I might add I am terrible at because I don't take many). I've noted that once I get the gun's speed up, that extra weight helps keep it going in the split half-or-less second I have to pull the trigger.
For snipe I like a gun that lets me get on the bird quickly before it starts "juking." A between the hands weighted gun works well for me here.
For rail, I've learned that a gun balanced to the rear works well. I also shoot guns that have more drop than my usual high-stocked guns work well, as often the birds get up close and drop almost immediately. (A gun that you don't mind getting muddy is also a plus.
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For the record, though, I can miss birds with any gun balance, and prefer to do so with a Parker.
