I would guess much of it depends on the diet of the prey animal. Eating the contents of a carnivore's stomach would probably be awful, but that of an obligate herbivore is probably not as bad, comparatively, since it would mostly just be plant matter, perhaps slightly fermented.

You only need to take a look at the difference between the feces of carnivore and herbivores. Cow dung or rabbit pellets really aren't all that bad. Wolf or otter feces, as two examples, is pretty vile stuff.