Here's my attempt to answer this question:
You should choose which site to ask your question on based on the kind of answer you're hoping to get, taking into account the users' fields of expertise.
So, a macroeconomics question posted on Economics.SE is going to get answered by people with an Economics background and is likely to be (on average) more mathematical and theoretical. The same question asked on Politics.SE is going to be answered by someone interested in politics, and answers are going to take more of a political angle: focusing, perhaps, more on the political implications of economics, or "economics as they work in the real-world" as opposed to theory.
One way to think about this is to ask yourself: "If I was at a University and I had this question, would I look for an economist or a political science professor?" Are you looking for an answer that quotes Economists, uses economic theory, and has equations? Then post on Economics. Are you looking for an answer that quotes politicians and pundits, that focuses more on the political implications, and, is, perhaps, a bit more "common-sense"? Then post on Politics.
Obviously, this isn't a real rule, but I think it's a good guideline.