Neither exist in a vacuum. At least not when it comes to humans and our brains. Emotions is just an idea/word that describes a certain range of human feelings that are loosely and roughly shared amongst us and loosely categorised and given labels. Logic is the term/idea given to reasoning/systems that adhere to a more strict principle/proposition of validity. So an attempt to reflect reality. Emotions tend to be more subjective and an expression of ones feelings, and can be true to that individual, its not an attempt to propose a fact about reality.
The tricky parts come in with peoples abilities to articulate and express logic and emotion, but also peoples ability to understand and appreciate those expressions as well. Communication is important with both ideas.
Another issue is people, generally overestimate how logical they are and greatly overestimate how emotional they are. Often, people will look down on emotions, because of the implication of lack on control, willpower, and the subjective influence and nature of emotions. Emotions don't change maths equations answers, however ironically many peoples negative attitudes towards emotion, can come from emotion or similar (ego is another variable that can be a strong factor) and many people lack the self awareness or competency to actually live up to the idea of how logical they are.
That being said, I tend to like logical people more than emotional people... but they have to actually be a logical person. Legitimately logical individuals actually tend to be emotionally receptive and considerate as well, and expressive. They just know when one os more appropriate than the other.