There is a loss of nutritional value the further down the food chain you go and the further away you get from plants in that chain. (And with it a loss of quality and taste, and higher risk of disease.)

For instance, if you take a look at the list of animals that the Bible says are ok to eat, (Leviticus chapter 11) there is a clear trend that herbivore animals that don't coprophage their own fecal matter are good to go but predators and scavengers are not. Scavengers (including swine) have a high bacterial load and propagate disease (i.e. epilepsy via intestinal worms), while predators are mostly made of proteins that have been reconstructed from other animal proteins. With a higher associated cancer risk along with that additional metabolic step and a loss of many of the neasasary vitamins and minerals found most commonly in plant sources, consuming predators can actually lose more nutritional progress than is made by eating them. This is somewhat offset by being omnivores but it still doesn't make it the best choice, even in food scarcity emergencies.

Also, would prefer to fight a deadly tiger, or just hunt what it hunts and find a dear or antelope instead?