I think most would start out at a search engine but the problem is that there are still a whole mess of sites out there that are not properly optimized. So one either misses these sites or comes across a niche directory by which they can then find listings of companies.
We run such a directory which is comprised of Arizona based construction and home improvement companies as well as realtors. The vast majority of sites listed in our directory would never be found in search engines because they have not been optimized. However, someone conducts a search, one of our directory pages shows up, they venture in and can now find a variety of companies.
That is one of the good uses of a directory IMO. Nevertheless, I myself would not go straight to a directory when searching but rather to an engine.