If your end-goal is to gain statistically reliable data that conveys authority and certitude, then quantitative is the way to go.
For example, you would use quant to measure product usage and brand perceptions and then track those metrics, statistically, over time. Or you may want to determine the optimal price point for a new product you plan to market. You would want qualitative data for something so precise.
Numbers are great when you want definitive data. But then wouldn’t you always go with quantitative research? Qualitative data is so “messy” and subjective. Who wouldn’t want to generate authoritative and certain results? It’s a fair question. But quant is not always right. It only works well when you’re ready to ask the hard questions and, even then, it only works for some strategic issues.