Barbarian C3 isn’t a bad class, but it won’t scale as well as other options along with Murmillo once you start transcending your weapon and getting very high physical attack…
The 2000% or more skill factor from murmillo’s attributes will make a huge difference once your weapon starts getting around 3k+ atk. Much more difference than what you get from Warcry (+400 atk) with lesser skill factor (around 1250% for seism, and that’s your strongest skill).
You would be able to 1-hit mobs outside ET with a barb3 build and heavily tuned up gears, but your skills would do about half damage (or even less) of a Rodel/Hop/Pelta build with Murmillo…
Once you get your Synchro Thrust’s Murmillo attribute to lvl 10, you will see Synchro’s damage, even being just skill lvl 5, will easily surpass the damage of Seism even with all 5 wild natures.