Dave, great question. I have a bit of a bias, given that I've spent the better part of the last 10 years designing and building microphones. But the reality is that the reason I chose mics rather than preamps is that I believe they are often the most important part of the signal chain in terms of determining what the track sounds like.
I'm assuming that the source and the room do not vary in this scenario. That is, given a single singer or guitar rig or drum kit in a single room, if you had to choose between mic, pre, converter, my ranking would be mic, then pre, then converter.
Placement IS critical, although in most cases, I'd rank that behind mic choice. Just to illustrate: a lot of home recording people have a closet full of "stupid deal of the day" condensers that tend to be bright and harsh sounding. There are not many placement tricks that would make those mics NOT sound bright and harsh. But you can put a better mic in just about ANY position and it will sound better than the harsh mic. Maybe that's less true on guitar cabs (to address Mark's point); I'm thinking of drums, vocals, acoustic guitars.
Needless to say, lousy placement can make a great mic sound awful. I have seen inexperienced artists "eat" a large-diaphragm condenser in a studio setting, and then wonder why the track doesn't sound good. "That's what works for me on stage!" Umm, your tongue shouldn't actually make contact with the mic's capsule during the take. #protip