For research done with the quantitative method, the researcher is typically an outside observer, merely collecting data and numbers. On the other hand, in research done in the qualitative method, researchers are typically more involved and participate in the study, as this helps them to draw better conclusions.
The data that's being collected is different in each method of research. Quantitative research relies on numbers and other numerical data. For example, "How much money did you spend on groceries last month?" It's looking for specific numbers from which to draw conclusions. On the other hand, qualitative research relies on words, pictures and objects. "For example, "Why do you spend the amount of money you do at the grocery store?"
In general, qualitative research tends to be more subjective, as researchers are more immersed in the research and must make inferences based on their observations. Quantitative research is more objective, as researchers use statistical data, surveys and questionnaires, things that are generally more objective.
How reliable the research is can vary on which research method is used. For qualitative research, the reliability of the research is often up to the person doing the research. How skillful is he or she? How rigorous was the research that was performed? On the other hand, quantitative research often relies on the quality of the measuring device or instrument that was used to record the data. Is it a good tool to measure what the research is aiming to find?
There's no right or wrong answer when discussing which research method is better. Still, this continues to be a hot debate. Which method is right often depends on what research you're trying to do, and which you feel is a better fit. Likewise, both methods can be done to ensure a mix of objective and subjective.