One is not better than the other unless you have a purpose in mind. A savings account is not a good choice if your purpose for an account is to pay bills or to have money quickly available for spending, using a debit card, for example. Those purposes are best served by a checking account, either a demand deposit or a NOW account.
A checking account is not usually a good choice for systematically setting aside funds in a rainy day fund, or for a specific savings goal in mind. It's also not usually a good place to keep funds that you don't need for normal spending needs, since a checking account normally pays no interest or little interest. A savings account is the usual choice for those goals. With interest rates at historic lows, however, the interest earnings difference between a checking account and a savings account may not be worth worrying about.
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