Why does Rainsford choose to confront Zaroff in the end rather than simply ambush him? What does this reveal about his personality?

That's a good question.  There isn't any textual evidence that directly tells readers why Rainsford doesn't simply shoot Zaroff in the back from a concealed location.  I think one possible reason is pride.  Rainsford wants Zaroff to know that he has been beaten.  Rainsford also wants Zaroff to know that Rainsford beat him.  If Rainsford took a sneaky shot at Zaroff, Zaroff wouldn't know that he had been beaten by Rainsford.  Zaroff would just be dead.  Rainsford is a popular hunter.  His skills have made him famous, and he still finds hunting normal animals thrilling. On the other hand, Zaroff pompously claims that he has grown bored with hunting the most dangerous animals in the world.  In a way, Zaroff seems to be claiming that he is a far better hunter than Rainsford because animals are not a challenge anymore.  By showing himself, Rainsford essentially says, "See, I knew you weren't better than me."  

Perhaps another reason has nothing to do with pride.  Perhaps Rainsford simply wants Zaroff to know what it feels like to be the prey.  Rainsford has been hunted to within an inch of his life, and nothing was fun about it.  Zaroff thinks it is great fun because he is not the one being hunted.  Rainsford's motivation might be just wanting Zaroff to feel what it's like to have the tables turned.  

A third possible reason deals with Rainsford's general character.  Rainsford is a reasonably moral man.  Zaroff presents a fairly logical explanation as to why hunting humans is acceptable.  Rainsford isn't even intrigued in the slightest.  He's appalled from the very beginning, and he calls Zaroff a murderer.  

"Hunting? Great Guns, General Zaroff, what you speak of is murder."

I think Rainsford's morality just won't let him shoot a man in the back.  That's why he confronts Zaroff instead of ambushing him.