hard to say. I think if you are not that high end and you have another melee class in the party, B3 is better since it is very “supportish” for a DPS build while not being ping based. I think HL 3 works more if you can afford more weapon and ping, the reason why HL3 could outdps B3 builds is because B3 has too much set up time needed while HL3 would usually have1 rank on Barb for a 15 seconds cleave debuff anyway, so they tend to combo straight up any boss, while skyliner with a good ping is very good.
Another thing is that, extending cleave debuff with warcry is pointless. even though it would be extended to 15 seconds with 1 cleave, the crit buff from cleave is still 5 seconds, so you still have to cast cleave again, which would replace that 15 seconds cleave back to a 5 seconds cleave. It’s more of extending other class debuff (like doppel debuffs) i think.
What I have been thinking is that they design Barb 3 for STR fencers though. They have 250ASPD from Frenzy, completely removing the need for DEX ASPD (most of fencer skills has ASPD). Extends Crit debuff from Balestra and/or Lunge Slash debuff. Gives 100 Crit to complement Epee Garde.