Is it worth taking Superior Technique battle style for Beast Barbarian Fighter multiclass?

I'm playing as a half-orc beast barbarian on 5th level. In our DM's world there are no magic resistances at all, so 6th level Beast Barbarian feature not really worth right now for me. So I'm thinking about multiclassing into fighter. My main weapon are claws and I have Dual Wielder feat so I can attack with them using BA.

Stats are Str 16 Dex 14 Con 16 Int 8 Wis 12 Cha 8

I haven't decided what subclass of fighter I want to take and I'm choosing between Battle Master and Rune Knight. I'm planning to go at least 3 levels into fighter, maybe 4 for ASI and campaign is set to go to 12-13th level, but might be a little further.

So is it worth to take Superior Technique even if later I'll decide to go Rune Knight route? Or it is not that good even on Battle Master? I know that I can take TWF for more damage on bonus attack, but that just doesn't seem fun enough for me.

Thanks in advance!