If the money is coming from professional bettors you want to bet with the money because it's considered "sharp" or "smart" money. If the money is coming from average Joes who are betting for fun, you want to be against the money because it's considered public or "square" money.
Smart money is capital placed in the market by institutional investors, market mavens, central banks, funds, and other financial professionals. Smart money also refers to the force that influences and moves financial markets, often led by the actions of central banks.