the concordia gun is a lot less powerfull then the one that hit goddard, but it could target ships, and the sivar weapon could not. and, as angel mentioned to tolwyn in that cutscene before they destroy the kamekh, they were not at full power, so they might short-circuit the powerplant.
a direct confrontation, in the favor of the concordia using its PTC, would depend on the effect of the shot, if one shot was not enough to take a hakaga down, the concordia(with drained recources) would be forced to retreat or need a miracle to win.
A tactical view, one would make several strikes, to "defang the beast", and move the concordia in to finish the massive ship off in a single shot.