I'd say Bron, as it is easy to beat on a corpse. Assuming, however, I went back in time to an instance when the original Sharptooth was still living, I have no doubt that Bron would lose. Bron himself made it clear that he is out of combat practice.
Littlefoot:
Eh, hey! How come we haven't seen any Sharpteeth?
Bron:
Sharpteeth are cowards. Look how many of us there are. A Sharptooth would never attack a group this size.
Now, Bron's account of the herd's origin makes it clear that it's been around for some time. Shorty's depiction when the herd was just getting started was certainly younger than how he is shown in the present. He seems to show a lack of experience compared to other Longnecks we've seen in combat. He slid down that mountain to give his tail attack more force to take down that Sharptooth. However, with his size and weight, he cannot recover from sliding down such a decline very quickly, and you all could see the result. He left himself vulnerable with his powerful attack, limiting his defenses, ultimately allowing himself to be wounded in his leg. He had no reason to hurry. The Sharptooth was clearly heading for him, so he didn't have to be as rash as someone protecting another.
As for the original Sharptooth, he is still very much in sinc with battle. His combat skills are even arguably more advanced than any other Sharptooth we have yet seen. Bron seems stronger, but battles have more to do with skill than physical prowess. For example, a teenagrer can subdue a grown man if the teenager has been well trained in the art of battle. In video games, the bosses of levels are nearly always stronger than the hero or heroine, thus resulting in the need for strategy and quick thinking. If Bron wants to win against the Sharptooth, he needs to plan ahead, looking not just at his current actions, but what his actions will result in after they've been carried out. So in short, like I said, I do not believe that Bron would win. If any disagree with my logic, I welcome you to please speak up.
As far as a suggested battle from me, what does someone think about Chomper versus the young orange Sharptooth in the episode "The Lonely Journey"? Chomper may have little desire to fight, but that Sharptooth seems very dependent on his parents' involvement in his battles, so I'm curious to see who someone thinks will win in such a case and why the given victory is chosen. I find this a fair question. Many haven't seen the episodes, I understand that. However, some have not seen all the movies. Have fun.