Automines due to their versatility - you know you'll have a use for them after you're done with the asteroids. You don't have that guarantee when it comes to asteroid mining ships, and they are surprisingly expensive. Not as much as automated mines, but even the modules themselves cost more than normal, manned mining complexes and you'll need additional minerals for all the stuff associated with building a ship/base like armor, crew quarters, possibly engines and fuel storage.
The third possibility is to rely on civilian mining operations. You can read more about them on Aurora wiki (
http://aurorawiki.pentarch.org/index.php?title=Civilian_mining_complex ). However you cannot control their growth (which can be slow at the beginning) you need a colonized body (with population) for the process to even begin, and the civilian mines are established only on bodies with duranium present. And it costs money to buy those mineral of course.
All in all automated mines are the most reliable method of getting minerals from asteroids, and most other bodies in fact.