The following wiki links contain the "official" info on this subject:
Note: these pages have been updated January 25, 2019.
From what I can read in the two wiki articles it seems there is no benefit related to time and no reward (other than what you see in port in the honor to heroes tab) for achievements.
Potential damage taken is rewarded.
Edit by Saltface: Please read bullet 5 - It might explain why you earn less. There is a certain amount of ambiguity but it could provide an explanation
For ease of reference read excerpt below: