Surveys and interviews are both tried and true methods for discovering what your users want. They are straightforward, easy to understand, and easy to do.
At a functional level, surveys and interviews are just questionnaires. Whether you prefer a written or verbal format, the questions must be constructed carefully so that the correct—and the necessary amount of— information is gathered. If you want to ensure respondents make a clear choice, use multiple choice or true/false questions. If you want more experiential answers, use open-ended questions. Quantitative data is best gathered using questions that use ratings, like a 1-5 scale or "never to always" scale. Regardless of the information you want, create questions that will prompt helpful insights.
In terms of administration, interviews require more time and preparation. Surveys can be distributed in person, online, by mail, or phone. Online surveys can be finished remotely with no further effort on your part. Interviews, on the other hand, require some sort of face-to-face interaction. This can be accomplished in person, over the phone, or using video conferencing. Since there is a human element, body language and delivery become more significant in interviews. For example, if the interviewer asks a question in a negative tone, the interviewee may feel pressured to answer according to what will please the interviewer rather than according to their opinion.
A comparison between surveys and interviews is given below:
Surveys
Cost
Extremely cheap, digital just costs time, even paper surveys are easy to produce
Administration speed
As fast as you can, write the questions and send them out
Data reception speed
Delayed by completion speed, respondents likely to wait until deadline
Efficiency
Possibility of thousands of data points in a few days
Interviews
Cost
Require human labor, video equipment recommended, notes necessary
Administration speed
Must ask all questions in person, one interview at a time
Data reception speed
Almost instantaneous, answers given at time of interview
Efficiency
Maybe a half a dozen a day, more if you are willing to spend more