Well that depends on several scenarios, but you should start by asking yourself a rather simple financial question: Which number is greater? The return on your investment or the interest you are paying. For example, a Forbes.com article asks if you should invest $10,000 that you owe in credit debt into a guaranteed 1% interest from your bank or invest it into a possible 30% return from a small business endeavor?
The bottom line is that there are a lot of alternatives to consider such as the cost of the debt and the downside risks or over a given time frame. Moreover, there are also emotional points to consider as well such as how a particular outcome will make you feel. So when trying to decide whether or not you should pay off credit debt or invest, try to make your decisions with your head and your heart for the likelihood of a winning decision.