Pardon me for jumping in uninvited... but I figured I would add something not yet mentioned (I think.)
(This is abstract and hypothetical, pardon the lack of proper documentation.)
Earlier on it was stated that the Masamune was effective against Magus because It absorbed/distorted the energy of Lavos that permeated Magus's being. I propose that purpose be taken a step further, in that Melchior created the Masamune to be a 'receptacle' of Lavos power. Fighting fire with fire. The Red Weapon was the untuned form of Masamune, and thus was attuned to Lavos's energy when it was plunged into the Mammon Machine, thus 'completing' it, with Masa and Mune as a sort of 'guardian' or keeper of the absorbed energies.
As the battles continued, the Masamune absorbed more and more of the latent energy of Lavos. How Masamune Two of CT fits in (As I see it) would be that Cyrus's spirit joined with the blade and 'increased' the energy of Lavos that could be harnassed.
Frog faces off against the true form of Lavos with the others, holding the Masamune in his hands. One slash, two slashes, each one would have absorbed more of Lavos's power, pure and untainted (relative).
After Lavos is dispatched, Masa and Mune sleep, knowing that the threat is 'over.' Cyrus goes on to his great reward, reincarnated, or completely nullified as time sees fit. In their ignorence (and the two have litterally proven they are airheads) they figure no more Lavos, no need for the sword; little do they know that in fact Lavos still exists, albeit in a somewhat different form. Lavos takes over the Masamune while the two sleep, creating the 'Demon Blade' of CC out of the pulsing-dangerous energy that the sword had accumulated over time.
This could also explain why Doreen was so angry with Masa and Mune, who had been sleeping on the job, letting Lavos use the accumulated energies of the sword as a form of avatar for himself.
This would explain the dual nature of the sword somewhat, for while it would 'reflect' the will of the weilder, it would also have the will of Lavos acting upon it. It would take someone of strong will to balance the ying/yang aspect of the powers. Masamune is the positive aspect of the power. Demon Blade is the negative aspect of the power.
With this theory the Hero's medal that Frog was so attached to would in fact be Psychosomatic as earlier stated, as it would focus the intention of the weilder of the blade. This would mean the Hero Medal would NOT have to be the same for both Frog and Pierre. One must have an ideal to focus on, a banner to hold high and say "this is what I strive for." It would be a power to enforce the mental-positive Masamune aspect.
For those of you asking why didn't the Masamune aspect turn everyone who weilded the blade into a raving peace zealot, remember the intention of good has never theoretically been to dominate evil, but instead to create the balance that is necessary for existence to flourish. The reason why the Demon Form DID make weilders become death zealots and jealous is because the intention of evil is indeed to overtake and sway the balance in its favor.