I have never had moose. I dislike duck, goose, deer, elk... most wild game. Except rabbit. On one of my first trips here to South Dakota, I was at a restaurant in Hill City called the Bumpin' Buffalo and I just had to try a buffalo burger. I fell in love.
Bison is leaner than beef, so cooking it is an art. It is low in fat (like you described Moose), so the key is to sear both sides of the burger on high heat, then finish cooking on low heat. Go to medium-rare if you can stomach it. It is the most juicy and delicious burger ever. If you overcook it, you will end up with a dry hockey puck. I make mine medium-rare then top it off with cheese, bacon, and the usual (ketchup, mustard, lettuce, tomato, pickle). I tried changing the cheese to Bleu Cheese once and it was awesome.
Since then, I have studied the bison. More than tasty, they are a mighty and majestic animal. I just love them. They have an attitude of apathy. They are not afraid of anything and if you are in their way, or too close to their calf, you get one subtle warning. They will raise their tail. If you don't leave immediately, you will be attacked. Everyone who visits Yellowstone needs to know that.
Sorry, I'm rambling.