Everything you folks are saying is matching up pretty well with the descriptions I've found. Stratievskaya has a big long description of the ESE-EIE Kindred relationship here.
Here's what I ended up writing to my ESE friend, based on Stratievskaya's article and various other sources (including this thread )...
The ESFj type is known as The Enthusiast (also known as The Bonvivant), and I call the ENFj type The Dramatist (also known as The Mentor and The Actor). These two types have the same Base function (extraverted Feeling), which makes them both very passionate, emotional, and empathetic people. As with all Kindred types, this makes it very easy for them to understand each other and establish a connection. Typically the two find that their goals in life are quite similar, and they can respect each other's basic attitudes, which are quite similar to their own, even if the details are different. In the case of the ESFj Enthusiast and the ENFj Dramatist, both feel strongly about things like injustice and suffering, they can both be very empathetic to the feelings and struggles of others, and both want to make the world around them a better, happier place.
The two types tend go about it in different ways, however. The ESFj Enthusiast has a very positive, optimistic view of the world, but is often worried that something is going to go wrong and wreck everything, and tries to prevent that from happening. The ENFj Dramatist is the opposite: he has a very negative, pessimistic view of the world, but has hope for the future and is constantly fighting to make that hope a reality. If the Enthusiast plays the song of life in a Major key, the Dramatist uses a Minor key.
The ESFj Enthusiast is always trying to minimize trouble and conflict and unpleasantness, and create an atmosphere of emotional peace, harmony, and happiness: to her, life should be like a picnic, full of loving family and friends who are all happy and content and enjoying life. The Enthusiast works hard to try to reduce the amount of conflict and strife in her surroundings, and make that vision of life possible for herself and the people around her.
The ENFj Dramatist, on the other hand, does not shy away from conflict and unpleasantness -- to him, life is a battlefield, a struggle to overcome. Without struggles and conflicts to overcome, life can become boring for the Dramatist. Victory is always over the next hill, but even when he succeeds in his quest and achieves all of his long-term goals, he finds he is not satisfied -- he must conquer the next hill, as well. And so on.
After a while, this difference can become exhausting for both parties.
During the early phases of a relationship, the ENFj Dramatist is often entertained and even refreshed by the Enthusiast's optimism and desire to fill every minute of life with joy and pleasure. But after a while, the Dramatist starts to feel that playtime is over now, and we should start getting back to the really important task of fighting the eternal struggle of life. The Enthusiast's emphasis on the daily details of living, like health and comfort and aesthetics, starts to feel claustrophobic, restrictive, even oppressive at times. As far as he's concerned, there are more important things in life, grander visions which must be pursued, and all of these mundane small-minded details are just getting in the way.
For the ESFj Enthusiast, on the other hand, during the early phases, the Dramatist can often seem very noble and inspiring and heroic, questing after his grand vision of what life should be. His passion is infectious, and the Enthusiast can become caught up in his excitement. But after a while, the emotional battlefield of the Dramatist's life starts to be too much; enough battles have been fought, and now it's time to settle down and be happy and start enjoying life and living "happily ever after". But for the Dramatist, "happily ever after" would mean accepting the world as he sees it: dark and full of misery and unfinished quests. The Dramatist's tragic and melodramatic view of the world starts to weigh heavily on the Enthusiast, who feels that her happiness and enjoyment of life is being drained.
Another aspect is that the ESFj Enthusiast has great difficulty predicting people's actions. Much of people's behaviour worries and sometimes even frightens her, because it seems confusing and even inconsistent. She is always afraid of insincerity and treachery, because she feels unable to detect it. Unpleasant surprises in general are difficult for the Enthusiast to deal with, because of her inability to foresee what will happen. Consequently, she often seems to panic over nothing, hoping that the people around her will step in and help her and solve the problem for her. The Dramatist doesn't understand this at all -- to him, it seems kind of selfish and maybe even cowardly.
Neither type has very strong Logical functions, so neither partner tends to be very impressed with the other's logical arguments, and both find it difficult to come up with their own logical arguments to convince the other. They also have very different approaches to matters of practical business logic -- the ESFj Enthusiast tends to worry quite a bit about the small details, which the ENFj Dramatist finds short-sighted and pointless. But from her perspective, the Enthusiast sees the Dramatist's attitude to these matters as reckless and irresponsible. Ultimately, neither is able to help the other in this area.
My ESE friend seemed to think it was an accurate description of their relationship so far.