Mansun

The sword the Balrog used was flamed by his own power - a power fueled by spells & sorcery like which Gandalf had not experienced before in his wildest dreams, not even when faced by the Nine Nazgul. Do not try & pretend that a flaming sword is not one with flame due to some supernatural power.



But just look at what Wikipedia has to say of Balrogs:-

A Balrog is a demon from J. R. R. Tolkien's Arda legendarium. A Balrog (Sindarin for "Demon of Might"; the Quenya form is Valarauko) is a tall, menacing being in the shape of a man, having control of both fire and shadow. One was noted to wield both a flaming sword and fiery whip of many thongs.

The Balrog induces great terror in friends and foes alike and can shroud itself in darkness and shadow. It can only be defeated by some person or thing of equal power, and amongst its own evil allies is rivalled only in its capacity for ferocity and destruction by the dragons, but the Balrogs are more powerful than dragons.[1]

According to The Silmarillion the Balrogs were originally Maiar, of the same order as Sauron, Saruman and Gandalf.

Can the enhanced Witch King match such a foe? It appears not, since he would need to be at least in equal power to Sauron, Saruman, Gandalf & the Balrog of Morgoth to be so. This ends the debate once & for all - Gandalf, Balrogs, Saurman, Sauron are all essentially closely matched, that we know. The Witch King, however powerful a sorcerer, cannot fall into this supernatural category & must therefore be deemed a weaker opponent. The Witch King cannot kill a Maiar without being of equal power at least.