That's completely game-specific, actually.
If your game is in some very simple/discrete space, then moving divs around will do.
But if you really want to do more complex graphics without much coding, go with the standard for HTML5 games - the canvas element. Do note that many HTML5 game engines support DOM rendering, but I'm not sure to what extent, I doubt that you'll have that awesome canvas API at your disposal.
As for engines, refer to this answer: http://gamedev.stackexchange.com/a/32777/9736https://gamedev.stackexchange.com/a/32777/9736.
The only other comparison I can make between the canvas and the DOM is that the DOM is a bit faster, or so I hear. But really, nothing substantial.