Notes from the Japanese famitsu tooltips:
Overheat INcreases damage dealt by 20%. So you will probably want to Overheat immediately before/after applying wildfire.
Dismantle reduces ALL damage by 10%, not just physical
Hypercharge effects remain the same as ENG tooltips; Bishop reduces magic resist, Rook increases (seemingly) ALL damage received by 5%.

In addition to this though, it also states that Bard's Foe Requiem increases the damage enemies take by 3%, not reducing their outgoing damaging by 3%. In this case, MCH DOES actually have cause for concern in terms of being outshone by BRD.