I won't go into my expositing of what I think will happen in the plot, but I think it's very likely there are "good" dragons and "bad" dragons. Those who want to eat the world, those who don't. Different factions, if you will. Even if you think I'm full of it, it has been confirmed that one dragonshout is the ability to summon a dragon to fight for you. I'm not 100% positive it is like the dragons we have seen thus far, but regardless it will most likely be able to have some sort of aerial combat else they wouldn't have bothered to mention it. Thus, to my point: How would a dragon fight a dragon?
Using the Construction Set, we can set allegiances of humanoid races and even some creatures to be friendly or hostile to the player. Again, one way or the other, it is possible for a dragon to fight a dragon. When such a confrontation does take place though, will it be awkward? We've seen the techniques that dragons can employ like bombing runs, but we've seen very little of their ground tactics beyond fire-breath down towards their assailants. Is it possible that they will actually enact in different AI behaviors depending on their opponents? Obviously there are a lot of techniques available with fighting a player, but what if it attacks another beast creature like those giants? Will it even? There's a lot of guesswork here, so I guess I should have my own say on it.
Again, we really don't know what Bethesda has in store in terms of the story, but I would not put it past them to at least have one fight where two dragons try to rip out each other's throats. It might be scripted in order to alleviate work for coders, animators, etc. but I have a strong feeling that this spectacle will turn up at least once in the game. There may be a system specifically in place for these battles, thus indicating that there will be a multitude of them, but I have less hopes in full for that. I think it would be well worthwhile to have some mid-air combat animations specifically for this purpose (and melee can be handled in a straightforward way) to give us a sense of the creature's power.
If it's not in yet, it's not in, so this is about you all then. What do you think? Will Dragon vs Dragon happen? Will Dragon vs non-humanoid beast happen? Do you suppose there is a system in place to facilitate such things? Would there be a purpose?