Both Highlander C1 / Barb C3 and Barb C1 / Highlander C3 are good, but play out a bit differently.
Barb C3 is definitely going to be stronger early on, but as higher ranks are introduced, as well as monsters with higher defense, I feel that Highlander C3 will scale better due to Skull Swing.
That’s just a guess, and really, play whichever feels more comfortable to you.
Highlander C3 requires some setup/knowledge of enemies you’re fighting to bring out the best in your damage (i.e., can the enemy bleed, and if not, which abilities to prioritize using in what order… or how much distance you need to charge Cartar Stroke to actually be able to use it vs some enemies, which enemies using Cross Guard to stagger can help make dealing with them easier, etc).
Barb is easier since you know bosses can’t be stunned, so against bosses you typically use Cleave first and then use attacks. Against most mobs, Helm Chopper + Cleave is the typical combo. Seism is also nice, especially if you’re investing in Double Pay: Earn with 1-2 points since Seism seems to fake multi-hit so using the skill should only consume 1 charge but still do high damage.
If you play both, you’ll feel that Barb C3 is currently stronger, but over time I think Highlander C3 will continue to scale better unless IMC changes Barbarian buffs to go from “flat” to being % damage increases.
tl;dr
Barb C3 - Better AoE potential, nice buffs for the current ranks/equipment available, easier to play
Highlander C3 - Better Single-target and small group potential, Physical DPS Party support (Skull Swing), better defense (Cross Guard), harder to play effectively (have to know what can/can’t bleed for effective damage setups vs groups), will continue to scale better as mob defense increases.