Military command stations are good for dispersing small-to-moderate size enemy forces, and provide good defensive bonuses with the planetary munitions boost.
Logistics stations are excellent for mobility and stalling any grouping of enemy ships. It depends on what you need - some of the time it's far more useful to have that extra speed and slower enemy ships. Considering the case of sniper turrets and missile turrets, you get twice as long to shoot at enemies before enemies get in range. Depending on enemy force composition, logistics will allow some slow dispersion of enemy ships, giving the opportunity to sweep some fighters in to clear the bombers before the frigates can really respond, bombers in to clear the frigates before the fighters can respond, and frigates to clear the problematic armor types (composite/neutron/refractive, for example).
I use mk3 military command stations as frequently as I can because at the difficulties I play it's necessary to try to kill things as fast as possible - on a mk3 military command station planet mk1 turrets have the damage output of mk2, mk2 turrets have the damage output of mk4, and mk3 turrets have the damage output of mk6.
