The one major flaw with absolute positioning is that it does a poor job of accommodating differences in visitor text size preferences. There are times position:absolute can be very useful, such as within DHTML menus, but for everyday layout practices, I personally tend to find it quite lacking. Floating, margins and stacking elements is typically all a Web page needs, even the most visually complex pages.
Margins make more sense, because if you're trying to position an element somewhere on the page and you want to create space for it, you are in fact pushing the entire object in a certain direction. Using padding means you are not repositioning the object itself, but its internal contents, which is typically not what you really want to do. Therefore, margins are a more accurate way to achieve your objective. Oh, and margins are more consistent across browsers (minus little things like the 3-pixel jog or margin doubling on floated objects in IE, but these are VERY easy to overcome)