Predators have evolved many different hunting styles, and what works for one animal won’t necessarily work for another.

Lions aren’t endurance hunters. They get close enough for a short chase and one of them (if the prey is too large to be killed by a single animal) goes for the throat and attempts to strangle the prey.

If this is a large, strong animal like a zebra or buffalo, it will still have energy and its legs and/or horns are still an issue, so eating it alive is not an option. It’s safer to make sure it’s dead before tucking in.

Spotted hyenas (the other hyena species do prefer to scavenge) have a different hunting method with larger prey. They chase it over longer distances and wear it down. By the time they overhwhelm their prey, it’s exhausted and less capable of fighting back and injuring them.

Spotted hyenas’ jaws are powerful and great for crunching bone and disemboweling their prey, but they haven’t evolved to go for the windpipe like lions and don’t have the long, sharp canines to deliver the coup de grace.

Besides, those lions are probably not far away and—despite stereotypes to the contrary—lions scavenge a large portion of their diet from hyena kills.

So, it’s best for the hyenas to just eat straight away before they lose their hard-earned meal, rather than wasting time making sure their prey is dead. They’re not trying to keep it alive, though, and prey dies pretty swiftly anyway.

Although somewhat distasteful from the human perspective, the speedy disembowelment of the prey means that death often comes sooner than with the methods employed by other predators (for example, suffocation) and is an efficient means of eating which lessens the probability of the kill being lost to another predator

This is more the case for large prey, as I mentioned. Spotted hyenas are also capable of catching and killing smaller prey on their own