In MH1, the Blazing Falchion is actually much stronger than the Corona.
An upgraded form of the Djinn, the Blazing Falchion is a decent Fire Element Sword and Shield. However, it cannot be upgraded any further, making the Golden Falchion weapon line a safer bet for long-term use.
In Monster Hunter Freedom, the Blazing Falchion is created from the Red Saber and upgraded into the High Ifrit, an excellent but hard to get weapon due to its G-rank Rathalos materials.
The Blazing Falchion also appears in MH3 with a slightly brighter colored blade, higher fire element, better sharpness, and no slots.
In MH3, The Blazing Falchion is the strongest offline fire SnS.