If the larger pin has a properly shaped tip (smaller radius at the edges lager in the center, not a hemisphere), fits the hole well, and the hole has a sharp edge, it will not be a problem. The problem is that this is hardly ever the case for factory actions. Greg Tannel's work is excellent, affordable, his turnaround is quick, and I do not know of any disadvantage associated with the smaller tip diameter. For factory rifles, If I am not having an issue with pierced or blanked primers, I shoot them as is, and live with the cratering. My custom actions have the smaller pin tips, and I am glad of that, because I think that they have good ignition, and seem to be more tolerant of differences in pin and spring weights.
Once I had a double heat treat '03 Springfield that I accidentally overloaded to the point where the primer fell out when I opened the bolt. (a loooog time ago, and only once) Those actions have very heavy firing pin assemblies, heavier than any commercial action, and mine had been fitted with a the heaviest spring that strong hands could assemble. The bolt was a well made new '03A3 Remington, that had been made to the highest standard, of fit, the hole was very square, and fit the pin tip very well. When I examined the primer that had fallen out of the case, there was absolutely no crater. Think about that for a bit. Neither was it blanked or pierced. I would not choose to have a pin that was that heavy in any of my modern rifles, or a spring that was that heavy, but with those, and a firing pin tip that was the same diameter as the larger of the two you inquired about, that was the result.