First, emotional intelligence (EI) is something people posses (more so or less so) while overseas intelligence is something people gather by things they do. These things cannot be equated or compared anymore than oranges and walking can be equated or compared. What is true is that EI is used in discerning human characteristics of terrorists behavior and personality. This is something popularized on the TV show "Lie to Me" where those naturally perceptive of microexpressions detect tell-tail signs of surreptitious or agitated emotional states. In certain close-encounter situations, EI will certainly gain in importance when/if people's trust in employing EI skills and perceptions increase. Overseas intelligence will continue to become increasingly important to cover large bodies of human activity, movement and trends. In other words, oranges and walking are and will be equally important and needed as will both (1) emotional intelligence characteristics, skills and applications and (2) overseas data gathering.
I can't imagine anything being more important than overseas intelligence in fighting the international threats that we face as a nation. Perhaps emotional intelligence can compliment overseas intelligence, but we have to have information about foreign groups and activities to be able to counter such threats.
I don't think emotional intelligence will prove to be more important than overseas intelligence when it comes to Homeland Security. I do believe it will prove to be just as important as overseas intelligence. Emotional intelligence is something that complements all other types of intelligence and together they constitute a strong front against domestic and international threats.
The nation requires quality, accurate information on the activities of individuals and groups that may pose threats. The men and women on the ground who search out this information, who infiltrate groups, who watch individuals and groups, must have emotional intelligence to properly assess the motives of these people. They can also pass this information gathered overseas to the Homeland Security people on the front lines at home who inspect, question, and assess the people they come into contact with. These Homeland Security individuals must utilize their emotional intelligence effectively as they work with the information provided from overseas intelligence.