As noted with their individual descriptions Griffins and hippogriffs despise one another to the point where they'll attack each other on sight (and they can see for miles). There have been many specualtions for this animosity but none quite fit, it is true that they resemble predator and prey, but when you consider that they seek each other out it doesn't quite fit. One scholar suggested that it may be a matter of competition but even when competing for food they will stop hunting to fight...the best explanation is possibly that they originated as some form of magically created hybrid and that the magics used in their separate creations somehow cause this animosity as a form of compulsion. In any case no one knows for sure but many have witnessed this hatred first hand.