When people talk about cross breeding fantasy creatures, I always think back to a Xanth book. There was a love spring, and when creatures drank from it, they would exhibit the effects of the spring with the next creature of appropriate gender. This was their way of explaining pegasi and such.
Not every cross breed has to have both the weaknesses and strengths of the parents. Look at the pegasus. Let's say it was derived from a giant eagle and a horse. The eagle is a carnivore/ scavenger and the horse is a herbivore. Pegasi are herbivores, but is that an advantage or disadvantage? They do lack the claws of the eagles to grab onto prey or branches so that is a disadvantage. If you compare a pegasus with a hippogryph, they are very similar, could one be a mutated offspring of the other?
Before we start breaking out books on gentics and guessing which trait could be dominate or regressive, step back for a moment. Nearly all the creatures involved are fantasy, or at the very least, thier coupling will be. Make up something interesting that mantains the game balance and enjoy yourself.