IQ doesn't really have anything to do with it. IQ was developed (I'm sure) by the US military to define who was suitable to be drafted in. They were also used to screen immigrants at one point. IQ tests have a pretty dark test and very restrictive, intentionally so at one point.
It was never designed to assess more than what was deemed appropriate at the time based on the context they were used in. And they only assess learned/developed comprehension of a given subject/area. This means that naturally the highest scoring IQ tests would not be high scoring if that individual did not seek to increase particular comprehension in given subjects, such as the ones described in the test. If you never went on to study mathematics, would you score high in areas regarding this subject? If life went differently, would that mean you were rendered dumb because you didn't get given the same opportunity to learn something that you might have learned otherwise? So you're not really intelligent then. If intelligence is universal and can be measured effectively, you would be intelligent regardless of whether you study an advanced level of a discipline or not because that potential is always there.
IQ tests do nothing to accomodate for this.
As you can see, learned skills/comprehension is a very small percentage of what makes up an individuals intelligence.
Someone who has a high IQ might not be able to put a garden shed together but the person who can put one together is more in demand and considered more valuable. Whose the most intelligent? Likewise, emotional intelligence is very similiar in this way. Emotional intelligence defines our connection to our own emotional state of being, and with others. Someone with high IQ could completely lack emotional awareness and understanding of basic human experiences, such as experiencing emotions. Does that mean someone with higher emotional IQ and lower general IQ is more intelligent? It's very superficial when you begin to pick holes at what we consider intelligence. Most of it is based on academic intelligence, itself often severely disconnected from the whole gamut of human experience, potential and capabilities. Academic intelligence is basically the ability to store and regurgitate information. We perceive our intelligence based on how well we can adhere to a particular set of rules that define our academic studies. Lots of academics have immense understanding of their subjects but are incredibly lacking in their own personal capacities and abilities beyond being able to regurgitate information and adhere to a particular system and say and see thing as considered acceptable by those who set the curriculum.
We pride ourselves on certain beliefs such as academic education and general intelligence governed by IQ tests because in our culture and in the Western world this is how you are judged and how you judge others. Someone who never went to high school is usually looked at with anamosity whereas someone who did a PhD is considered superior to others. This doesn't actually explain the innate abilities of these individuals nor their limits. One conformed to the expectations of the culture and therefore is far more likely to be accepted and seen as a 'real' person, whereas the other didn't and consequently won't. It still doesn't really answer the question as to who is intelligent. Many high school drop outs are self made millionaires whereas many PhD students work at McDonalds full time and are still paying off their student loans. The high school drop out is more successful and arguably more intelligent in their ability to succeed and understand the landscape and then capitalize thus becoming rich and successful, at least in the ways in which we relate to success in our culture. We could go on forever describing the flaws in how we look at intelligence.
