I'm in agreement that the 209 primer conversion isn't better, if you get reliable ignition with a No 11 or a musket cap.
There is a reason shooters generally get better accuracy with a small rifle primer than a large one, and in some cases, small pistol primers work even better than small rifle primers (.22 Hornet). You want enough flash to reliably ignite the charge, but too much isn't better. Too much can cause the powder and bullet to begin to move before the powder fully ignites and the small differences in volume and pressure at the moment of ignition cause small differences in burn rate that cause small differences in velocity, which impacts accuracy.
If you are an experimental type, load a ball with no powder, then set off a 209 primer and see how far the ball is pushed up the barrel compared to a No 11 or a musket cap. You'll get a similar difference with a powder charge in the barrel, with the powder moving down the bore before it ignites.