The choice is not about preference or rigor. It follows directly from the kind of question being asked.
Use quantitative methods to measure
When the question is how many, how much, how often, or whether a difference is statistically detectable, quantitative methods with an adequate sample are the right instrument. They support representative estimates, disaggregation and comparison over time.
Use qualitative methods to explain
When the question is why, how, or under what conditions, qualitative methods provide the mechanisms and context that numbers cannot supply. They are also essential for exploring unfamiliar topics before an instrument can be sensibly structured.
Use mixed methods when you need both
In practice most consequential research questions require both. A survey establishes the scale of a problem; interviews explain the behaviour driving it. Sequencing matters: qualitative work before a survey improves instrument design, while qualitative work after a survey explains unexpected results.