Presumably this depends on where the front line is, assuming a DropShip is actually equipped with command facilities. Depending, it might not have those really for whatever reason.
If you have well secured LZ, you probably don't want to move your Droppers even as the front line is moving further away. So, take a MHQ to the front line. Or if the front line is in terrain that is completely unsuitable for DropShips.
(Going to assume here that comms between front line and the LZ can be disrupted so having a command post near front is a good idea.)
Also, a HQ is target, depending on the era and combatants, DropShips might get treated as non-combatants so you might not want to make them targets by using them as HQs (not sure if this actually happens, perhaps among the Clans?).
A planetary garrison force is like spread across the planet but its DropShips, if any, could be concentrated in the primary space port. So those spread out forces could use MHQs.
Another reason to use MHQ is for mobile bases, for guerrila forces and the like. You know, you have some of those mobile field repair gantry things, a mobile field hospital, and a MHQ for communications.
Personally i see MHQs as more akin to modern communications platforms (like the Finnish "Viesti-Pasi" ("message-Pasi"), an APC equipped with communications equipment for command and signaling) rather than a field headquarters usually.