What realistic change do you think could be made to make weapons feel different from each other?
Secondary stat bonuses? Passives for each weapon type? Talents? If it were up to me you could straight up swap yoir entire Mastery passive dependent on what weapon you're weilding.
How I would handle it though:
Each class gets a passive effect for each of their primary weapon types. (Warriors don't need passives for Bows, for example) These are small effects that activate whenever you cast any GCD spell. Different effect depending on whether the spell targets an ally or an enemy.
Example, Paladins:
Polearm (Enemy) Heals you.
Polearm (Ally) Inflicts Holy Damage against the target's attackers.
Sword (Enemy) - Bleed.
Sword (Ally) - Heal-over-time.
Mace (Enemy) Gives you an absorb shield.
Mace (Ally) Gives the target an absorb shield.
Axe (Enemy) Ignores % of armor.
Axe (Ally) Increases the damage of the target's next attack.
Shield: Grants you an absorb shield.
Off-Hand: Inflicts Holy damage to your attackers.
Just make it as effective as a tertiary stat, and tie it to Transmog instead of actual equipped weapon so drops aren't screwed up. ***Something***.