Enemies have different resistances. Some will have very little physical resistance, but more fire resistance.
For instance, your BKS will do a crap ton of damage to most of everything in the Demon Ruins while your Bastard Sword will only do its' physical damage minus any physical resistance the enemy has.
The BKS is regluar/thrust. If you use the strong attack button, you do a (incredibly slow, so I wouldn't advice doing it too often) thrust move with BKS. Thrust attacks generally do more damage than regular attacks. The Bastard Sword has no such attack, it is only a regular. This varies from enemy to enemy as well.
Your BKS also has scaling, C in strength and E in dexterity. When you ascend a weapon to a elemental path, it loses it's stat scaling, which means the Bastard Sword is limited to it's 294/294 damage output. Your BKS will go well beyond it if you invest souls into strength.
Your Flaming Bastard Sword +10 can be useful on some enemies who have a weakness to fire. Take Ornstein & Smough for instance. They are both vulnerable to fire, so that Bastard Sword would certainly come in handy, especially if you plan on taking down Ornstein first.