They both have their advantagaes and disadvantiges
The Lion is best - not just because it's a much more powerful animal, but also because it runs in packs that cooperate together and apply strategic chasing techniques.
although the cheetah is faster lions are stronger
The cheetah is the fastest land animal in the world. Other fast animals would be horses, dogs, antelope, bears.
The lion
In a fight between a cheetah and a lion, the lion would likely win due to its larger size and strength.
a lion, cheetah, any large animal
Lion,cheetah,tiger
leopard, lion,tiger
Lion no contest. A Cheetah would be destroyed in this mach up its not even 1 fraction in size of a Lioness and Lions are the top predators in the animal kingdom. The Lion has this one.
meat eaters
Lion,Cheetah and Tiger.
If you want to argue for the lions, you talk about their coordinated efforts, general strategies, etc. If you want to talk about the cheetah, you can talk about their physical might (speed, endurance, etc.). I think if you want to argue for the lions, you argue that they are the more intelligent and therefore the more /skilled/ hunter, while if you want to argue for the cheetah, you argue that they are /physically/ stronger than a lion. Though, I'm not sure if this is a very scientific approach... Maybe if you bolster your case with statistics and the size of the animals the lion/cheetah hunt in relation to its own size? :D