But, actually, he chose a stag because it was large, powerful, and fast. It could survive a werewolf attack (assuming the worst case scenario happened). When the Marauders told Remus they were animagi.
“I feel I owe you another explanation, Harry,” said Dumbledore hesitantly. “You may, perhaps, have wondered why I never chose you as a prefect? I must confess… that I rather thought… you had enough responsibility to be going on with.” Harry looked up.
Seriously though. James Potter was a much better man than Severus Snape. Whereas James bullied Snape while they were kids and then grew out of it, Snape used his position of power at Hogwarts to bully children.