I watched the show as kind-of a guilty pleasure, but got bored with it eventually. The fights seemed too implausible in many cases. I also never could quite get over its similarity to the Roman death games, though of course no one was actually killed in these.
I can easily understand the show's appeal to the public. Zookeepers are constantly peppered with questions about animal fights. Would a lion beat a tiger? How about a gorilla? Would a gorilla beat an orangutan?
Among zookeepers, the question of importance isn't who would win a fight. It's who will start one. Animal death matches might make exciting TV, but they don't exactly reflect optimal welfare.
The challenge is especially real in safari park settings, where large numbers of different species are housed together. The challenge for curators and collection managers is to stock an exhibit that recreates the African savannah or Asian steppe without bloodshed resulting.
Predators, obviously, are out of the picture. The lions and cheetahs at the San Diego Zoo Safari Park may have a panoramic view of the herds below, but that's as close as they get. Herbivores require careful mixing too, however. Hippos are seldom included in safari parks, in large part due to their irascible nature (I've read of hippos killing zebras). Zebras for that matter are no angels, especially males. White rhinos are typically okay, black rhinos... not so much.
Even relatively docile giraffes can be problematic in some causes... even if it's only because they are provoked. A bull giraffe at one zoo was constantly harassed by an obnoxious male eland, an antelope the size of a large cow. Eventually, the giraffe had enough and with one swing of its neck, sent the eland flying like a golf ball.
Conflicts are most likely to break out between the males of similar species, which may view each other as rivals. They are especially likely to break out during rut, the period of heightened aggression that prepares males for the breeding season. The birthing season is also a risky one, as animals may display hostility to the young of other species, whereas they would ignore the parents. Mothers, in turn, may react aggressively to innocent curiosity from other species.
There is a lot of trail and error that goes into creating a safe, well-balanced safari park. While each species tends to have a characteristic demeanor, a lot of the success comes down to the individual personalities of the animals involved. When in doubt, I always recommend erring on the side of caution. A beautiful exhibit is a wonderful thing, but not at the expense of animal safety.