NEW YORK ( TheStreet) -- Thinking about closing your account with your big, bad bank? Does that mean you are placing a greater premium on service over safety?

TheStreet's readers said last month in a popular poll that they would leave Bank of America ( BAC) over the $5 debit-card fee

But some readers agree that when it comes to keeping their money safe, they would rather bet on a bank that is too big-to-fail. In a poll conducted by TheStreet last week, 84% of 146 readers said they would rather put entrust money with a big player that is tightly regulated, than risk losing their money with smaller firms that tend to escape regulatory scrutiny.

Clearly, when most people are asked to make a choice between safety and service, they will probably choose the former, so the poll results aren't particularly surprising.

But it does show why big banks like Bank of America and JPMorgan Chase ( JPM) are not too worried about reports of customers abandoning them on Bank Transfer Day .

People who have a lot of money to lose, like companies and high-networth individuals, are likely to stay put with their big banks.

The failure of MF Global ( MFGLQ.PK) may not have posed a risk to the financial system but it has raised concerns about whether smaller firms that fly below the regulatory radar are the best place to put your money.

Two weeks after the broker-dealer filed for bankruptcy, there is still no word on what happened to more than $600 million that has gone "missing" from the firm's customer segregated accounts. Regulators are investigating whether MF violated a basic rule that requires companies to keep client money separate from the firm's own in order to protect clients' assets.

Now MF's clients and creditors are battling each other as each party tries to recover their money first in the bankruptcy process.

The incident has reinforced calls for regulation of risky practices by proponents of regulation such as the Volcker rule.

Such regulations might limit the ability of big banks to generate high returns to their shareholders. But with regulators breathing down their necks, too-big-to-fail banks are less likely to flout basic rules, such as segregating customer accounts.

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