I knew of a company that did a per head price. The problem is the higher the salary, the harder the role is to fill. They ended up going the percentage route eventually. I am sure there is a better price structure, but flat percent (20) seems to be the standard pricing these days.

Finding a Senior Dev is much harder than finding a Junior one, so maybe they charge a percentage for simplicity because the former simply has an higher salary and it would be too complex to charge different flat fees depending on the position category.