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Why this distinction? Being emotionally intelligent is a prequisite for being a highly professional, intellectual and a good speaking person.
There is no a such a best leader but if you would say relatively beeter I would say the later which is an intelectual and good speeking guy could be more preferable as a leader.
Emotions, empathy, communication and being optimistic are some of many traits those differentiate a Leader from a Manager.
It aprears that you have the answer to your question by the way you have formed the question itself.
Thus my comment is: why stress on emotions ? sometimes your gut feeling is better than any analysis or forecast.
To be a real leader, you have to get all those qualities and more.
However, it's depends on the Industry of the organization.
I think good leader require all those4 qualities