Some missions / quests have a bonus task to complete. What are the advantages to completing this task before handing in my quest? Better loot? More money? Anything else?
Completing bonus objectives contributes to the Compl33tionist challenge, which in turn gives you badass ranks.
There are five levels to this challenge, similar to most other challenges:
Level Badass ranks gained --------------------------------------- Level 1 10 Level 2 25 Level 3 45 Level 4 70 Level 5 100
I can say with certainty that completing bonus objectives adds to the cash reward, and was true for each quest i tested.
If you look at the quest menu before completing a bonus objective, take note of the stated cash reward, then go and complete one (or more) bonus objectives. Now return to the quest menu and the new, increased dollar reward amount should have changed.
As far as I've been able to tell, this (along with the “completionist” challenge, and sometimes a bit more dialogue) appears to be the only benefit of completing the bonus objectives. I have never seen any direct experience point increase, or any kind of correlation to the stats of quest reward items. The only other possible benefit may be an increase in drop rates for quest related enemies, but thats just total speculation, and I have not noticed any significant change (and with BL2's drop rates, testing this would be very difficult, and would require literal thousands of test runs).
In the case of the Mission Assassinate the Assassins the rewards went from 10900XP to 10900XP+1330$ per objective. (TVHM)