If you are asking two questions then here is my answer.
Large or small firing pin?
I cannot shed any light, is the weight saving noticeable? Will the lock time improve your accuracy to a noticeable degree hunting?
If you are asking will a case small primer type case be an advantage?
It would allow you to run a hotter load. That's what they say.
Is the gain noticeable for a hunting load. I don't have enough experience to say but it just raises all the comments regarding game not being able to tell the difference in 100fps,
If you want to screw every bit out of a cartridge find a variant with a small primer pocket, Ackley Improve it and use a long barrel to get the most of that given cartridge.
Then, find the next one up and reconsider it all over.
Decisions, Decisions,
I settled on. .280ai btw, 26" barrel and it's just built on a Tikka,