Which is more important for a technical communicator? Writing skills or tool skills?

The 'intelligent' answer is both on an equal basis. You can tell this to interviewers; they will nod in agreement. But what exactly is the reality? In companies, it is the tool guys that rule the roost whether it is MS Word, FrameMaker, Robohelp, or Flare, and not the guy with excellent writing skills. If you have average writing skills, but excellent tool skills, you career can go places. You are one of the promising people in the company from a non-technical background.