IQ is typically a measurement of a person's objective, unemotional knowledge. It doesn't measure personal feelings, just knowledge of facts. Emotional intelligence is a more subjective field, concerning a person's ability to understand and interpret the emotions of others in a fair and consistent manner. Therefore, the value of each quality varies depending on how they are intended to be applied.
For example, a researcher does not need excessive emotional intelligence to perform well; instead, knowledge of facts and how to find and correlate information is valuable, and so a high IQ would be helpful. Similarly, a scientist should be able to perform complex calculations and quickly understand scientific concepts, which would be measured by IQ.
A psychiatrist, however, works with both scientific and emotional tools, and should be able to understand the emotional states of the patient; in this case, while also likely possessing a high IQ, emotional intelligence becomes more important because of the fragile state of the patient. Social workers, caregivers, and other human-centric fields all require excellent emotional awareness, and so the sum total of knowledge (IQ) is not as important as the ability to identify and interpret emotional states.
In summary, both are important depending for different reasons.