Economics, in theory, has very little to do with finance. It is the study of how a society uses limited resources, like energy, food, a currency, etc. It often factors in political and demographic realities. Finance is the study of... Finance, the financial markets, basic accounting, basic statistical modeling. I say in theory because plenty of economics programs focus heavily on business realities, but in general it's a question of whether you're more interested in the work you'd do as an economics major or as a finance major. You can tell the difference by looking at the courses in an average economics and finance program. Finance is generally considered more preprofessional, but it is my opinion that economics generally results in more well-rounded students that are stronger in math.
The rule of thumb is if you're interested in working in "business," and you're deciding between economics and finance, your best bet is to pick the program that is better at your school. Despite the fact that the core courses are different, oftentimes the electives overlap which makes a double major almost redundant.