You have an ideal situation, believe it or not. What I would do in your place is pick up a digital vernier to measure the firing pin protrusion on both guns. You'll need to remove the butt stock to do it. Press the lower pin firmly forward (it's lightly spring loaded) and measure how much of the pin sticks past the breech face. If you get slightly varying measurements take the average of 5 measurements.
Start with the "good gun". Then compare those results to the problem one.
If what we've discussed is causing the issue, the problem gun's lower firing pin should be protruding somewhat further than the good gun's. If it isn't, then something else is causing the problem, possibly a rough surface on the pin, etc.
If you do decide to shorten the pin, don't simply make it the same overall length as the good one. The critical thing here is how far it sticks past the breech face. There may be some variation in the thickness of the breech face between the two guns, which will influence how long the pin needs to be to stick out "x" thousandths of an inch. Try a small change first, 0.005" shorter might be enough to do the trick. If you go too far, you'll get fail-to-fires. Mine seemed to work ok at 0.052" protrusion.
One more thing. The FP retaining pins on your Browning are small straight pins with a serrated head on one end to hold them from shifting. Pick up a cheap jewelers eye loupe and look closely to see which end is which.
Only drive them out one way, in other words tap on the non-serrated end, so the serrated end comes free first. Put them back in the same way you found them, and either take pictures or make careful notes as you go so you don't forget which way they were.
Don't ask how I know this.. lol.
I got mine from Brownells, it was an ordeal dealing with UPS. I'd order them through a gunsmith if I had to do it again, or Browning Canada if they will sell them.