Most funds are managed. That means that there is a manager who is in charge of that fund and it is her job to study the market every day and buy and sell stocks in the fund to try to maximize gains. Within the category of managed funds there is a pretty wide range of management styles. They go from highly actively traded mutual funds to those that are mostly buy-and-hold stocks.
The managed mutual funds are generally more costly than unmanaged funds because you have to pay for the manager. The more actively managed funds would therefore be more costly than the more passive buy-and-hold funds. The advantage of a managed fund is that it has the potential to gain more than a passively managed fund or a non-managed fund.
Non-managed funds are best represented by the index funds like the Wilshire 5000 and the Nasdaq 100. These funds buy a certain segment of the market and hold them. Changes in stock holdings occur very rarely and the returns tend to be fairly stable and consistent.
If you were to look at managed funds versus non-managed funds you would probably find that some of the managed funds show a much better return than the index funds and some show a much worse return. In other words, the non-managed index funds are more of a middle-of-the-road investment, more conservative and generally safer.
An actively managed fund is better than an index fund only if the fund is well-managed. This is the trick. An actively managed fund can bring in excellent returns or it can lose you money. You really need to investigate the fund, its history, and especially its manager. With a managed fund, you are really betting on the manager as much as you are on the basket of stocks that make up the fund.