I could go with 2 different ideas here.
1, I kind of liked the idea of characters adopting the weapons of the world they are in,they would have to adjust to using new gear, unfortunately this would require them to change weapons in almost every chapter. (I can imagine my Avatar picking up a heavy cannon and the recoil throwing her across the room)
2, Weapons go by hit points. For example, a sword attack in Dynasty Warriors that would slice a man in half in real life would only take down maybe 10% of their HP. Or like in almost any Star Wars game a lightsaber strike would mean instant mutilation in the movies but for all the duals in the games you still have to hit your enemies a few hundred times with a lightsaber before their health is reduced to zero. So in that sense a Katana and Lightsaber would do equal damage, despite how much more advanced the lightsaber is.