This is a very intelligent question. More things separate Rainsford and General Zaroff than make them alike for most of the story. For example, even though they are both hunters, Rainsford would never think of hunting humans, like Zaroff. However, at the end of the story, something interesting happens, which may suggest that Rainsford is very much like General Zaroff.
Towards the end of the story, Rainsford decides that he must do something other than flee or wait if he is going to survive. He, therefore, decides to go on the offensive. He will go to Zaroff. This surprises Zaroff, because when he gets home he sees that Rainsford is waiting for him.
Zaroff admits that he lost the "game." At this point, the reader wonders how the story will end. The reader is not left to wonder. Rainsford never slept a better night in Zaroff's bed. The implication is that Rainsford killed him. This makes Rainsford as bad a Zaroff. In this sense, they might be the same.
Here is the text:
Rainsford did not smile. "I am still a beast at bay," he said, in a low, hoarse voice. "Get ready, General Zaroff."
The general made one of his deepest bows. "I see," he said. "Splendid! One of us is to furnish a repast for the hounds. The other will sleep in this very excellent bed. On guard, Rainsford." . . .
He had never slept in a better bed, Rainsford decided.