Two handed war axe vs Great axe: lose 0.7 weight, 4 length, 3 damage for 1 speed
Persian war axe vs Persian battle axe: lose 0.2 weight, 5 length, 3 damage for 1 speed
Bardiche vs Great bardiche: lose 0.2 weight, 14 length, 1 damage, for 2 speed
The second choice is clearly better in most cases and this is reflected in-game. Out of all of these weapons, the only one I see with any regularity is the Great Axe, but I pretty much never see the first ones at all (except for Lumetta with the Two handed war axe). Making the weaker versions balanced (with appropriate price tweaks) would make them much more attractive choices and would increase general in-game 2h diversity which is at the moment sorely lacking. Instead of having 3 straight up better versions of almost the same weapon, players would be presented with the choice between length/damage/weight and very slight speed/balanced. This would also make some degree of sense visually and "realism"-wise, as the currently worse versions are all shorter and have smaller heads.
side note: the Persian war axe might need a 1 speed buff, otherwise the Bardiche is simply superior