A series of government-sponsored studies has touched off a new controversy in U.S. educational circles over the emotional question of whether private schools are better than public ones.

The battle lines for what promises to be a long conflict are shaping up as follows:

The Rev. Andrew M. Greeley, a Roman Catholic priest and sociologist, reports in a detailed study that minority students from comparable backgrounds perform better in Catholic schools than in public ones. The differences are widest for blacks and Hispanics from the poorest and most educationally deprived families, he says.

But the National Center for Education Statistics, which reviewed the findings, has questioned them in memos circulated to experts.

University of Chicago sociologist James S. Coleman reported in another study based on similar data that Catholic and other private schools provide a better education overall than public schools and in some respects are less racially segregated.

But, it was learned yesterday, the federally funded National Assessment of Educational Progress has concluded after a massive study of the reading abilities of 100,000 children aged 9, 13, and 17 that public and private school children from similar family and economic backgrounds do about the same quality of work.

Meanwhile, the department's National Institute of Education has just released a study of private high schools that concludes:

"Public schools must begin to look at those aspects of private schools that make people willing to pay for them," and suggests that "public schools could organize themselves along curricular and philosophic lines that parallel private schools."

The NIE study also says public schools could "introduce widespread open-enrollment arrangements, and they could permit school facilities and parent associations wide latitude in running the program and the school itself."

The NIE said "The pendulum is swinging toward a public concern over issues that private schools represent."

At stake in the widening debate is more than scholarly disagreement about the quality of education in public and private systems.

Public schools supporters fear that some findings could be used to strengthen the case for tax credits to families paying tuition to private or parochial schools.

President Reagan has pledged to support tuition tax credits, but the issue promises to be an emotional and divisive one in Congress.

Some opponents, such as Albert Shanker, who heads the American Federation of Teachers, have warned that such aid would lead to the destruction of public education in the United States.

On the other hand, the NIE study, which takes no stand on the tax credit issue, is optimistic about the future of public schools, declaring that "access to the public purse should provide public schools with a solid, competitive footing."

Other enemies of tax credits say the aid could increase segregation by encouraging more middle-income whites to shift children from public to private schools.

One scholar said yesterday that the credits could lead at the high-school level to the kind of public-private schism that now exists in higher education.

Coleman, however, sharply challenges that assumption in his report, although his interpretation of data also is under fire from his critics in educational circles.

Coleman maintains that the tax credit enticement would cause minorities to increase slightly their share of enrollement in private schools.

Greeley's findings challenge a common assumption that minorities enrolled in private schools do better work than their public-school counterparts because they represent the "cream" of minority communities.

Greeley acknowledges that "it is the children of the more affluent, educated and more successful minority-group members who attend Catholic schools."

However, he reports, blacks and Hispanics who have the lowest incomes and are least advantaged show the biggest gains over their public-school counter parts while in Catholic schools.

Yesterday, Greeley accused the National Center for Education Statistics of a "sneaky, dishonest trick" in circulating a "hasty " evaluation critical of some parts of his work. Greeley charged that the NCES had covered up his findings by not running studies that would have confirmed his central thesis.