I don' t have a dictionary handy but using the MSWord Thesaurus-

Trophy:
memorial of victory
prize
memento
award
citation

I think the first one says it all. It is a memorial. It has to do with the road to get there and the battle that day in the field. I can' t go out today and play in the superbowl, I have to do my time and earn the chance. the playoffs etc. so yes this has a longer road and is a bigger prize because fewer have the chance,

If taking a large buck required a long trail of shooting smaller bucks it may mean more. But anyone " could' walk out their back door and kill a world record with with their first arrow shot.

IF you can' t tell me a good story it is only an impressive animal not a trophy.