Exchange-traded funds are closed-end, e.g., they have a finite number of shares that are bought and sold on a stock exchange. Frequently these types of funds can trade at a discount or a premium to their net asset value (NAV, or the total value of that fund’s holdings at any given point in time) so if you are paying a premium to NAV in order to purchase the fund, that could work against you.
Mutual fund shares are purchased directly from a fund complex, and that fund complex generally issues new shares of a mutual fund in order to fulfill buyers' orders to purchase that particular fund. The disadvantage here is that as more and more buyers purchase shares of that fund, and more shares are consequently issued, the performance of that fund can be diluted. In the long run, however, we find no great advantage to purchasing one or the other.