A lot of times, I hear "huuur opposites attract", and well, I used to think that. At least a little bit, and I tended to waver about it too. I then found that being too much alike and too different are equally bad, BUT likes go to likes. "Healthy people attract healthy people and unhealthy people attract unhealthy people" (Heartless-Bitches.com). Two halves of the same coin is often the term. SO, in the case of Axel/Demyx, it's not that they're opposites, they really aren't.
Let's first look at the elements: Fire and Water.
Now, most people will say that they're opposites. Actually, that's not quite the case. Fire and Ice are opposites. Fire and Water are actually quite similar when you think about. Water puts out fire, but fire can boil water and make it hot. Both elements can be hot, except that fire stays hot and water is generally cold, but can become hot. Fire is always light, but water reflects light, so it's "light" in its own right(huur, I rhymed). Fire is always in motion, and so is water, but in some forms CAN be still. BOTH elements can be very destructive and KILL people. However, water is often far more devastating as you can't put out water, you can only try to "contain" it. Fire is simply painful(putting it mildly) if the smoke doesn't kill you first, but is only widespread when it isn't controlled. Fire gives life, and water brings it. Fire and water make steam. Yay. Oh, but no creatures live in fire. Water, on the other hand, has many creatures, and some of them are scary.
So, what does that prove? Probably not much, except that while they're obviously different elements, they clearly have similarities.
Now for their personalities. No doubt they differ, but here is how they are alike(only problem is that very little is seen of Demyx, and so I can only go by my own interpretations/opinions):
1. Both are manipulative. Yea, sure it's in different ways, but they both tend to manipulate in order to get whatever it is that they want. Demyx plays the "lost puppy" role(at least some fanartists see that), and Axel plays a much more sinister role--Satan.
2. Both have shreds of decency, as they, along with Roxas are the least disgusting members of the Organization.
3. Both respond to music. Demyx, well duh, and no one calls Axel "Flurry of Dancing Flames" for nothing.
4. Both are intelligent. Demyx is moreso than people think and Axel, is of course highly intelligent, except he came from the "school of hard knocks", so he isn't one for "book learning." Neither is Demyx.
5. Both fight very well, only Axel is clearly more of a "warrior" sort, and Demyx fights only when he absolutely has to.
6. Both are charming, except Axel's spell wears of quickly because he is MEAN.
7. On that note, Demyx tends to be a little more subtle--period.
8. Both show their 'feelings' strongly, and more than anyone else in the Organization, except maybe for Roxas.
9. Both are good-looking(hahaha had to say it).
10. Both are "radiant" in their own way, and tend to be the more "humorous" members of the Organization. Axel is sarcastic while Demyx is more of a "dork".
11. They both love/hate each other. A nice, stable relationship. Heh.
And hell, that's all I can think of. Since Demyx gets little so little screentime in Kingdom Hearts, it's just hard to say with him. We'll probably find out more once the new games come out.