Mining modules only cost as much as regular mines, with some premium from other ship modules (armor and crew quarters). They're way better bang for the buck (and especially for the Corundium) than automines, but they only work on a limited number of bodies.
Also you can assign a +mining captain to an asteroid miner, the bonus of whom will stack to the "planetary" governor (and of course sector command).
Bottom line: If you have asteroids with a decent mineral occurrence (and I always have had those), asteroid miners can be a great choice, irrespective of tech level.