Do you prefer to conduct qualitative or quantitative research for what you are solving for?

It depends on how much information you already have to start with. I've found (and the Pragramatic Institute agrees) that you need to do qualitative research first. Then, once you have some idea, you can formulate that information into a quantitative assessment. But you need to have enough information to know what to put as the survey response options, for example.

Both qualitative and quantitative research methods have their advantages and are often used in combination to provide a comprehensive understanding of the problem being solved.

Qualitative research focuses on exploring attitudes, behaviors, and motivations through methods such as interviews, focus groups, and observations. It provides rich, in-depth insights into the underlying reasons behind certain phenomena and can uncover nuances that you didn’t know about.

Quantitative research, on the other hand, involves collecting numerical data and analyzing it statistically to identify patterns, correlations, and trends. Surveys and experiments are commonly used to gather quantitative data, allowing for the measurement of variables and the generalization of findings to a larger population.

You generally use Qualitative research when you want to do an exploratory study wherein you are looking to understand the underlying factors while quantitative studies are done when you have a good understanding of the underlying factors but don't know their individual and relative importance. 

In my experience a combination of both gives the best results wherein the qualitative study feeds into the quantitative study.