Author's note: I myself am an INTJ, therefore Ne is not in my main function stack. I have compiled the best information I can from what I found from Career Planner, The Career Project and Quora answers, however, I cannot provide any personal anectodes.
Extraverted intuition is an extraverted and perceiving function, basically the extraverted equivalent of introverted intuition (Ni). While Ni works more convergently, Ne works divergently, which means that Ne users can easily expand on existing ideas and are good at seeing many possibilities. Ne users are good at coming up with new, creative ideas and solutions. While Ni makes a few, more long-trm connections between data, Ne makes more connections, but these tend to be more short-term and can be less reaslitic.
Another difference is that while Ni works with extraverted sensing (Se), Ne works with introverted sensing (Si). This means that Ne/Si users draw on past experience in order to come up with their ideas and connect data.
For Ne users, coming up with ideas is a very active process. I've observed this with my ENTP friend, who is excellent at brainstorming. Ne users like to use charts, diagrams, or talk out loud about their ideas.
Another thing I've found is that Ne users are more likely to be 'jacks of all trades', having a wide variety of skills and hobbies, some frequently jumping from one hobby to the next, whereas Ni users tend to have fewer hobbies, but they would often spend a longer time with each hobby than Ne users.
I've also found this description of Ne: "Bursts of ideas that are inspired from a premise, and they are connected to each other. A person with Ne can usually come up with several ideas at once, right then, right there. Different from Ni that needs to let things sink in and come up with something moments later or even days/weeks/months later."