Re D&D falchions - I would treat it like a bastard sword as exotic 1-handed, martial 2-handed, keep the stats.
Re broadswords & longswords - the D&D straight-bladed, pointy-ended single-hand sword seems to resemble the early-medieval swords used primarily for thrusting, to penetrate chainmail, ie primarily a thrusting weapon not slashing. This kind of sword is ineffective vs plate armour. The AD&D '2d4' broadsword seems to be a shorter, heavier-bladed slashing weapon. For stats if you want to differentiate it I'd recommend 2d4 damage crit 20/x2. This makes it about as effective as the 'longsword' and keeps the 1e/2e stats.
Re katanas - these are obviously not masterwork bastard swords except in the PHB. They're a good bit lighter, to start with, with a curved edge. I'd use either normal longsword stats or 1d8 damage crit 18-20/x2, you can make it an exotic weapon when wielded one-handed if you want to maintain balance vs longswords, or just make it cost a lot more.
Re broadswords & longswords - the D&D straight-bladed, pointy-ended single-hand sword seems to resemble the early-medieval swords used primarily for thrusting, to penetrate chainmail, ie primarily a thrusting weapon not slashing. This kind of sword is ineffective vs plate armour. The AD&D '2d4' broadsword seems to be a shorter, heavier-bladed slashing weapon. For stats if you want to differentiate it I'd recommend 2d4 damage crit 20/x2. This makes it about as effective as the 'longsword' and keeps the 1e/2e stats.
Re katanas - these are obviously not masterwork bastard swords except in the PHB. They're a good bit lighter, to start with, with a curved edge. I'd use either normal longsword stats or 1d8 damage crit 18-20/x2, you can make it an exotic weapon when wielded one-handed if you want to maintain balance vs longswords, or just make it cost a lot more.