People who went to cut-rate legal clinics aimed at middleclass Americans said they were more satisfied with the way their lawyers represented them than were clients of traditional, higher-priced lawyers, a study by the University of Miami's School of Law shows.

The study - the first ever done to establish whether the supermarket-style firms sacrifice quality in cutting legal fees - found that legal clinics do measurably better work in the one area it examined the most closely, payments for child support in divorce cases.

It found that husbands represented by legal clinics negotiated child support arrangements that, on the average, were $16.37 less per payment than those represented by other attornys. Similarly, wives whose lawyers were from legal clinics received $38.05 more in monthly child support payments.

The study, reported here yesterday at the opening of the American Bar Association's 10th annual meeting, was made by Timothy J. Muris, a former Federal Trade Commission attorney in Washington who is now assistant professor of law at Miami, and Fred S. McChesney, a fellow at Miami's Law and Economics Center. That center financed the research.

They compared the attitudes of clients of the Los Angeles legal clinic of Jacoby & Meyers, which pioneered the concept of offering cut-rate legal aid for such routine problems as simple divorces and wills, with the attitudes of clients of the law firms that follow traditional practice. The two groups of clients had the same economic resources.

Similiar legal clinics have multiplied across the country during the past year as a result of the U.S. Supreme Court ruling in June 1977 that ended advertising bans on lawyers. For the most part, these clinics depend on advertising to bring in the high volume of business needed to keep their fees down.

"It has often been asserted," said Muris and McChesney, "that if advertising does lead to lower prices it will also lead to lower quality."

They said their study suggested the opposite. "Despite lower prices . . . the quality of the clinic's services is demonstrably better than traditional, non-clinic firms providing the same services," they asserted.

Nonetheless, a hearing yesterday of the ABA's commission of advertising showed the profession is still bitterly divided on the question of lawyer advertising and arguing over the fine print of new regulations.

Even those lawyers who are prepared to accept the Supreme Court ruling voiced fears that advertising will drag the profession of law into the realm of ordinary tradespeople by allowing what one attorney, Kurt W. Melchior of San Francisco, called "the wide open and contentless hucksterism we are beginning to see."

Melchior, head of the California Bar's Committee on Professional Responsibility, agreed that the Supreme Court ruling which said that bans on lawyer advertising violates an attorney's First Amendment right to free speech "must be given a fair chance . . . but some of us are very nervous about it."

A more extreme view, offered in a letter to the commission from R. M. Gholston, an attorney from Franklin, Ind., was that only incompetent lawyers will advertise.

"It's bad enough to have idiots running ads in newspapers," he wrote the commission, "but this nonsense (allowing television advertisements) absolutely takes the cake . . . I guarantee you that if this occurs, it will be the incompetents that will avail themselves of it, not the decent ethical members of the profession."

On the other side, Stephen Z. Meyers of the Jacoby & Meyers legal clinic said the ABA over the past years consistently has taken "regressive stands" against new methods of delivering legal services, and if it fails to allow advertising on television it will "be reduced to a trade association for corporate firms."

Meyers said last year's ABA's recommendations on lawyer advertising have been largely ignored by states across the country, especially California, New York, Ohio, Maryland and the District of Columbia, all of which have large urban populations.