I'd say they are quite independant. Ideally you need both of them but in reallity it is better to have some tests rather not having them at all.

If I were dragonchild I would teach QA-staff to use some non-programmer friendly tool (<shameless plug>HTTP::WebTest</shameless plug>) and ask them to start writting functional tests. Conserning unit tests: when you have big pile of cra^H^Hcode it is hard to implement missing unit tests at once. In most cases you have no time and/or motivation to do this work. However it is not hard and IMHO sufficient to start writting unit tests for all new or changed code.

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Ilya Martynov (http://martynov.org/)