FrogReaver
The most respectful and polite poster ever
Piercer feat
I did some math on piercer feat. Not every case, but should be enough to get an idea. The chart details a 2 attack PC and what outcome on the first d4, d6, etc that they choose to reroll. The highlighted value is the optimal decision. As you can see it's fairly close to using the reroll anytime when the damage might increase (2 or less on a d4, 3 or less on a d6, etc). I then combine the effect it grants on critical and the reroll at the bottom.
On the Champion
Champion over 2 attacks with d6 weapons and piercers only adds ~2.86 dpr from piercer feat. A non Champion adds ~1.92 from the feat. ~0.87 comes from the rerolls. Altogether even on the champion extra die crit damage for a hand crossbow character is adding just a little over 1 dpr per attack. The reroll adds a little less than 1dpr as well. Add about +1 damage per extra attack.
Compared to GWM
At level 5 the GWM on a Fighter just adds about 6*.6 dpr = +3.6 DPR. It provides similar enough early numbers to GWM. As you add more attack or find advantage from other sources the value of GWM starts to skyrocket. Still, for a level 5-10 campaign, piercer isn't looking bad in comparison.
Note on Battlemaster
Superiority dice at level 5 can deal a total of 18 damage if used on damage maneuvers per short rest (ignoring precision as without a very high damage attack, it's not nearly as good).
If a short rest period was 3 rounds: +6 DPR
If a short rest period was 10 rounds: +1.8 DPR
With Piercer: +3.8 DPR to + 9 DPR
Battlemaster wins
At least for most levels 5-10. About equal in the worst case but potentially massively ahead anytime there is not alot of combat rounds per short rest. Essentially it takes magical weapons with +die damage to really start equalizing.
Elven Accuracy
Champion with Elven Accuracy helps, but this is also a ton of feats to try to grab, sharpshooter, elven accuracy, crossbow expertise, piercer. Even with the extra free feat, that's going to be a level 8 fighter to get it all.
Conclusion
Assuming the same feats on both builds I'd go with Battlemaster just because of the control options. Damage wise I think they will be close enough. Champion by the 2nd fighting style and a +die magic would could actually get an advantage here IMO. I think later tier battlemaster will be better just because the superiority die every turn is likely to be better than champions heroic inspiration given your steady stream of advantage from vex.
		
		
	
	
		
	
				
			I did some math on piercer feat. Not every case, but should be enough to get an idea. The chart details a 2 attack PC and what outcome on the first d4, d6, etc that they choose to reroll. The highlighted value is the optimal decision. As you can see it's fairly close to using the reroll anytime when the damage might increase (2 or less on a d4, 3 or less on a d6, etc). I then combine the effect it grants on critical and the reroll at the bottom.
On the Champion
Champion over 2 attacks with d6 weapons and piercers only adds ~2.86 dpr from piercer feat. A non Champion adds ~1.92 from the feat. ~0.87 comes from the rerolls. Altogether even on the champion extra die crit damage for a hand crossbow character is adding just a little over 1 dpr per attack. The reroll adds a little less than 1dpr as well. Add about +1 damage per extra attack.
Compared to GWM
At level 5 the GWM on a Fighter just adds about 6*.6 dpr = +3.6 DPR. It provides similar enough early numbers to GWM. As you add more attack or find advantage from other sources the value of GWM starts to skyrocket. Still, for a level 5-10 campaign, piercer isn't looking bad in comparison.
Note on Battlemaster
Superiority dice at level 5 can deal a total of 18 damage if used on damage maneuvers per short rest (ignoring precision as without a very high damage attack, it's not nearly as good).
If a short rest period was 3 rounds: +6 DPR
If a short rest period was 10 rounds: +1.8 DPR
With Piercer: +3.8 DPR to + 9 DPR
Battlemaster wins
At least for most levels 5-10. About equal in the worst case but potentially massively ahead anytime there is not alot of combat rounds per short rest. Essentially it takes magical weapons with +die damage to really start equalizing.
Elven Accuracy
Champion with Elven Accuracy helps, but this is also a ton of feats to try to grab, sharpshooter, elven accuracy, crossbow expertise, piercer. Even with the extra free feat, that's going to be a level 8 fighter to get it all.
Conclusion
Assuming the same feats on both builds I'd go with Battlemaster just because of the control options. Damage wise I think they will be close enough. Champion by the 2nd fighting style and a +die magic would could actually get an advantage here IMO. I think later tier battlemaster will be better just because the superiority die every turn is likely to be better than champions heroic inspiration given your steady stream of advantage from vex.
			
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