After having watched a bit of film, Kanter is a power forward type who can post and face. He has an excellent shooting stroke out to 18 feet, and could develop three-point range easily. Cousins has some of these skills, but is not nearly as polished in his face-up game as Kanter is right now. Kanter has an adequate handle for a big man, but I'd be reluctant to say it is better than Cousins'-- maybe not quite as good in the open floor.
Kanter has that little "crab dribble" thing he uses to get to the basket from about the free-throw line that reminds me a bit of Brandan Wright (former North Carolina Tar Heels forward), and he really has a good back-to-the basket game, but he is not even close to as powerful on the block, nor as quick-footed as Cousins. Kanter does run the floor well, and is a bit less likely to loaf than DeMarcus, but give me the Big Cuz with the ball in his hands anywhere in the open floor over Kanter.
Kanter is a much better passer out of the post, though, and his court vision and activity are excellent. Kanter has a really good touch around the rim, and is similar to Cousins in the way he refuses to give up on offensive rebounds. I think this is where the comparison popped into people's heads, because he does remind you of Cousins the way he attacks the glass.
Kanter is a much, much better player than I expected, and his game is remarkably well-rounded and sophisticated. As such, his rate of improvement may not be as great as Cousins in his first year, because Kanter has slightly less raw athleticism but considerably more polish to his game. He lacks Cousin's remarkable wingspan, so he tends to jump when defending rather than staying down like Cousins was so good at doing. At the same time, he is a more advanced position defender than Cousins right now, and moves his feet pretty well when defending the post.
Overall, I question the assessment that Kanter is a lottery pick this year. He is farther along, basketball-wise, than Cousins at this point in his career, but he lacks many of the rare physical gifts that Cousins possesses, and his feet are nowhere near the same league as DeMarcus'. He will be a fine player, maybe even a one and done first-rounder, but if he goes in the lottery, it will be much later than DeMarcus Cousins.
[UPDATE 19:10] Three related videos: