What kind of mutual fund are you talking about?
A mutual fund is simply a group of investors pooling their money to buy stuff. That stuff can be stocks, bonds, commodities, short-term loans to companies (called "commercial paper"), and probably other things I can't think of at the moment. Every year, the mutual fund then passes along to the group of investors any earnings or capital gains and losses that the stuff inside the mutual fund has experienced during the year (or quarter or month).
I'd guess you're talking about money market mutual funds. In that case, the interest paid by the investments in the fund still gets passed through to you as the owner of the mutual fund. When you receive the interest, you can choose to reinvest it back into the fund if you wish. I believe most money market funds pay dividends monthly, so your compounding period is going to be monthly.
In theory, the rate of return would be higher (up to a point) if you could reinvest your interest payments more frequently. However, the mutual fund itself isn't going to pay you dividends every day or every hour, so you're kind of stuck with whatever payout schedule the fund has.
If you're looking at comparing mutual funds, just compare their 7 day SEC yield and pick the highest one.
In today's low interest rate environment, honestly, it's not going to make any appreciable difference unless you've got millions to invest in them.