Off the top of my head I can think of the following 'perks' for each type of weapon.
Very simple and they don't add any new mechanics to the rules, just spread the wealth a bit - both pluses in my book. Strong guys are going to want to use the bashing weapons to get that strength bonus but might possibly carry around a sword to use in case they are fighting skilled opponents so they can increase their defense.
- Only swords can be used to block as per the blocking rules.
- Axes/hammers/clubs add full STR bonus as damage like two handed weapons do.
- Pole-arms get the distance thing and first strike against rushes.