I think using them together is crucial. Qualitative research gives you insight into what you should look for through quantitative research. It's important to start with some basic qualitative research (talking to a few customers) and then scale it through quantitative methods (analyzing logs).
i liked poking about think-aloud protocols (https://en.wikipedia.org/wiki/Think_aloud_protocol) - jeff shrager always said to wait until they're swearing while they're doing whatever it is you're having them do and then you know you've started doing a think-aloud protocol properly.
