As this AP article via Boston.com
reported, money market fund yields are extremely low:
Normally you’d expect money funds to earn 2 percent to 4 percent a year, but now the average yield is down to around 0.03 percent
Savings account rates may be low, but they are sure a lot better than money market fund yields. One advantage with money market funds that the article mentioned is that when rates do rise, rates tend to rise faster in money market funds compared to bank accounts. However, with money market fund yields around 0.03%, they're going to have to rise a lot just to equal today's rates on most internet savings accounts and reward checking accounts.
Note, please don't confuse money market funds with bank money market accounts