dark mousyBoth Dark and Krad were created from a piece of artwork know as the 'Black Wings'. The Hikari family created Black Wings. When the Hikari would create a piece of artwork, it was rumored that they would put human souls into their works. (Creepy, huh?) They didn't stop there; they wanted to create the ultimate LIVING piece of art. The Niwa family attempted to steal the black wings. When life was being blown into black wings, the ritual was interrupted. Dark and Krad were born from this, Dark being mixed in to the Niwa genes, and Krad being mixed into the Hikari genes.
Dark and Krad have a somewhat complex relationship. Whenever Dark and Krad meet each other, they automatically start trying to kill each other. Nobody really know why exactly they fight. They most likely fight, because they say that Dark is the 'darkness' then Krad is the 'light'. So pretty much that means that they are fighting a constant war against each other, the Dark Versus the Light.
In response to the above, it has now been stated by Krad that he tries to kill Dark Mousy and Daisuke because he considers them a Ďthreatí to his existence. What this means, Iím not sure. But there is more than likely a reason behind it, I donít think Krad randomly decided that Dark or his host are just going to kill him when they get the chance. We actually could go so far as to say that Krad is paranoid if we wanted to. It all depends on how you want to look at it.
In the past there could have been some event that happened that made Dark and Krad enemies. But they were probably already enemies because the soul of the Hikari was in Krad, and the soul of the Niwa was in Dark. As we know, the Niwa and Hikari were considered enemies because the Niwa constantly stole the artworks created by the Hikari. This was bound to cause some hatred between the two and this is why Krad hates the Niwa family so much.
Without a doubt (at least in the anime) they HATE each otherÖ or at least Krad hates Dark. Though it seems to me as if Krad is bothered by Dark getting close to others. Either he is jealous because Dark is capable of having a somewhat normal relationship with others. OR, Krad wants Dark all to himself! ... I really like that theory. xD