I apply in Maine and New Hampshire every year. I have yet to draw in either State, but you've got to play to win. NH is a straight draw without bonus points. I think I recall that the draw odds for a nonresident are about 1 in 60 to 1 in 65 range. One chance for $25.
Maine uses bonus points which essentially are extra chances in the draw. The unusual thing about Maine is that they give you an extra point (chance in the draw) for each year that you are unsuccessful, but they also let nonresidents buy as many chances in the draw as they want. I don't buy a pile of chances each year, I usually limit myself to 6 which I think costs $35. You can enter with as few as 1, or you can buy them in blocks of 10 for $55 each.
Generally speaking, the moose population and success rates go up in each State as you head north. Both States publish the prior years success rates on their websites. Good luck to everyone!