There's a problem with "BiS" for WAR and that's that there are actually 2 sets you need: one for OTing, one for MTing. OT one should maximize STR and Determination, whereas the MT one should maximize VIT and Parry. Allagan Battleaxe is definitely the better axe for MTing as it provides extra VIT, STR, and weapon damage as well as enough accuracy to afford using the Allagan Flanchards (higher parry) - this is also helpful for OTing as those same flanchards provide +11 Determination. HQ crafted acc are also BiS for OTing as they provide, y'know, more STR/Determination.

Basically, your BiS changes for what you're doing in that fight. Don't try to stick to one set if you can afford to use different pieces.