I've recently (like in the last 3 weeks) lvl'd both an axe barb and a sword barb but I got to say I personally enjoyed the axe barb more just because of a more optimal aura stacking. In my experience as a Sword barb you would either go A2 merc with Might + Conc, but missing out on Fanaticism due to no Beast, or you go for Faith merc and miss Conc aura and get a lower Might aura (using Last Wish).
Versus say a sword barb with A1 Faith merc an axe barb using X wpn + Beast, and A2 merc obviously, would get Fana with Beast (though it's pretty low dmg by itself as a weapon not counting aura), and a higher Might aura (20 at least vs LW's 17, even higher due to Might not having a cap or is that bs?) + conc aura.
Versus a sword barb with A2 merc, like you suggest, the might aura is going to be the same, but the sword barb will be lacking Fana.
I haven't done the maths if axe barb with X wpn + Beast and an A2 offensive merc with Pride would be higher damage, but wouldn't it be common sense (since the auras in this game are fairly strong) that since the axe barbs always will get one more aura than sword barbs, they'll always be slightly better? And slightly more expensive probably. Also take into account (this isn't as important due to the flat number added from Grief to avg dmg) that PB's overall have a significantly lower avg dmg than Zerker axes, 47.5 vs 33. Again, that gets offset with Grief slightly but yeah...
PB's do however have a higher innate weapon speed but I'm questioning if that's gonna matter with a good geared axe barb bugging weapon speed and having Fana. And pb's don't break.
Never the less, you have done a good job on your topic and you are for sure a better theorycrafter then I am so I'm probably wrong.
10/10 for your work mate.