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Depends on what you want to do. +spd -res is pretty decent if you're going Slaying Axe+ build or anything else that isn't Brave Axe+ really. He can kinda avoid doubles if you invest enough spd into it. Speaking of which Fury is great on him with his balanced stats. +atk -res if Brave Axe+.
I would personally go with +Spd or +Def if I were to build him. -Hp regardless, since his base 46 HP is way overkill, and HP is almost always the least important stat.
+Spd Barst is obviously going to be more offensively-focused, boasting an offensive spread of 54/45 at +10 (assuming +Spd refined Slaying Axe+ and Fury), while also having a decent 37 defense. He's essentially going to be a discount Raven with slightly better physical bulk. Still, 54/45 before a seal/buffs is decent.
The other possibility is making him into a meatshield with +Def. +Def/-HP Barst at +10 is going to have 52 HP, 51 Atk, 36 Spd, and 41 Def (assuming +Def refined Slaying Axe+). From there, you still have the flexibility to add in a defensive A slot and Seal, which could be things like Steady Stance + Fortress Def Seal or double Close Def. His defense is pretty good, and you could alternately run Slaying Hammer+ to really screw over armors in high tier arena, though Zelgius and Tharja would still give you problems. Even without regards to armors, though, his stat spread makes him excellent for dealing with the majority of bulky blues and greens.
Or here's another thought. +10 +Hp/-Res Barst with any refine and Fury + HP5 Seal will have 63 HP. Give him Wrath, Vengeance, and a Slaying Axe, and he'll have a 2 CD vengeance (which accelerates by -1 every turn when under 47 HP) and his special will deal 41 damage when he's at 1 HP (before factoring in his regular attack stat). It's stupid, gimmicky, impractical, high investment, and suboptimal, but it's definitely a hilarious concept. You could alternately give him a Giant Spoon and his special would be dealing 51 damage at 1 HP, but it'll be a 3 turn CD.
I have the feathers to make any unit a 5*+10 but the only unit I have enough copies of is Barst! Unfortunately his max arena score is 740 and my other 3 arena core units (dragons) all score 742. If Barst actually got a decent prf I’d be pretty happy since it would make him score 742 and I could instantly build him.