With this statement, I think you are coming from a place of cultural bias. I find that men and women are more alike than "radically different" with emotions, with similar emotional needs and wants (perhaps to different degrees, but there is much variation within gender, I feel). However, in some societies, how they are allowed to recognize, validate, and meet those needs and wants are strongly shaped and regulated. For example, in Roman society, a woman who would want fame and prestige from being seen as virtuous would try to become a Vestal, or show extreme fidelity to a husband publicly. Today, a surer route to fame and prestige will look very different.
I don't think you know what is being meant here by emotionally intelligent. An abusive person who cannot control their anger, or someone who abuses alcohol to cope with their feelings in a detrimental way is an example of someone who is not emotionally intelligent. A person who can, most of the time, empathize with you, and can give and accept help and advice based on your goals putting you first (and explicate and communicate situations wherein they have to prioritize themselves or someone else), and knows their own goals and emotions and what they need, are some of the traits and behaviors of what people refer to as an emotionally intelligent person. Sometimes you see the term emotionally mature, which means the same thing.