Hello!
It depends on several factors, as the Falcon Longsword and the Falcon Battleaxe are items for specific hunts. For example, the sword will be better suited for hunts where the monsters are weaker against physical damage, while the axe is more suitable for hunts where the monsters are weaker against energy damage.
Currently, you have a 4-skill advantage; apparently, the sword skill is higher?
In my opinion, I would use the sword because the skill is higher.
Determine your hunts, see which hunts you will do in the future. Both are good, axe and sword, but the best decision is to choose one of the two and focus on training only one skill.