EQ: Contradictory or Banal?

EQ vs. IQ: Without having read the zillion selling book, I've always found this Emotional Quotient stuff to be both highly plausible and a conceptual mess.

For example, you can rank people on a scale of how well and how quickly they understand and can manipulate other people's emotions with displays of your own emotions. Autistics fall at one end of the scale and, say, Barbara Walters and Oprah Winfrey at the genius end. There's some correlation to IQ -- the famous autistic college professor Temple Grandin can figure out other people's emotions to some extent through sheer logic, and I'm sure Barbara and Oprah have quite high IQs, but it's also different enough than it's reasonable to think of as somewhat separate from IQ.

But then a lot of this EQ stuff you read is just advice to think more rationally and coolly about your own emotions, and your ability to do that is obviously highly correlated to IQ. It's good advice, in the mode of Ben Franklin and Alexander Pope, but it doesn't fit much at all with the first, Barbara-Oprah, meaning of EQ.