A popular question I get from many students related to research methodology is whether quantitative methods are better than qualitative ones. This is an ongoing debate and there seems to be a lot of confusion. Here is my opinion.
First of all, we must understand that the philosophies behind the two approaches are quite different. It is essential to understand the ontological (i.e. the study of being or existence) and epistemological (i.e. study of the way knowledge is obtained) orientation within one’s personal paradigm. That should be the first step.
Most quantitative research follows a Positivist paradigm, where the data collected is believed to be the true measure of reality or representative of the population and aims to produce findings that are generalisable. This contrasts with interpretivism, which mostly applies to the isolated incidents.
According to the hypothetico-deductive methodology, scientific inquiry proceeds by formulating a hypothesis in a form that could be falsified by a test on observable data. However, if you got the hypothesis wrong in the first place, the results will be wrong as well. In other words, "Rubbish in, rubbish out".
In my own field, Marketing, my observation is that currently, the positivist paradigm seems to dominate with most papers published in the top marketing journals following a quantitative methodology. Taking a closer look, research on more traditional issues in consumer behaviour, such as purchase decision making, persuasion, regret and affect, are positivist. While on the other hand, several modern consumer research often uses interpretivist methods that focus on particular consumption experiences and angles of consumer behaviour - sometimes giving totally new insights which might not be possible using a quantitative approach.
As many studies have indicated, the claims of universalism and generalizability used by Positivists can be criticised. For example, no two people are the same - even twins are different in many ways. It can be argued that rich insights into this complex world are lost if such complexity is reduced to a series of law-like generalisations. Sometimes when we do so, we miss the big picture.
In other words, using a quantitative approach is just one way of looking at a problem and may not always give accurate results. In my personal opinion, qualitative methods are not superior to quantitative approaches and vice versa. They may be actually complementary and it is the reason that mixed methods are increasingly becoming popular.
Note: This is the slightly modified version of my answer which was first posted on Quora.