I ran two Nightfalls and three Weeklies last night with a full fireteam of three every time.

Did you get rewards both times? Because if so, then I'm seriously doing Nighfall non-stop for the rest of the week.

I knew that Fatebringer did extra damage in the VoG, but had no idea it worked outside, so I've been doing some testing (you know how much I love testing things).

Seems like I've found the answer. You probably remember seeing posts a couple months ago explaining why Explosive Rounds weren't worth it, but just in case - Explosive Rounds do the same non-precision damage as normal rounds, but spread across the initial impact (2/3rds normal damage) and the explosion (1/3rd normal damage). With precision shots though, the explosive damage doesn't multiply like normal, so you only do 7/9ths of non-explosive precision damage (3x[2/3]+[1/3]). This means that using Explosive rounds is of no benefit unless you're fighting tightly packed clusters of enemies like Thralls.

All of that is now untrue.

I don't know when this change was made. It might have been as early as that major patch that buffed Scout Rifles and "nerfed" Auto Rifles, but at some point Explosive rounds were buffed. I have no idea if it's intentional or a bug, but Explosive Rounds now give you a direct DpS increase

Against regular, red-health enemies, Explosive Rounds do 1.5x damage on non-precision shots (Initial impact deals full normal damage, plus the explosion deals an additional 50%).

Precision damage vs. normal enemies and all damage against yellow-health is the same as non-explosive rounds, so there's no drawback (with the exception that Firefly and/Or Outlaw won't always proc on what appears to be a precision kill - sonetimes it's the explosive damage that does the actual killing).

This is not just on Fatebringer, but also on other weapons!

I don't have a checkpoint inside the Vault, but anecdotally Explosive Rounds seem to do even more damage in there, regardless of weapon - again, not just Fatebringer, though I need to test this.