The 23 million public school children who participate in the federal school lunch program tend to be better nourished than those who get their noon meal elsewhere, but the chief nutritional benefit that 3.5 million poor students receive from the school breakfast program is that they eat a meal they otherwise might skip.

These were among the conclusions of a two-year Agriculture Department study of 7,000 families participating in USDA nutrition programs that provide breakfast, lunch or milk to students.

About 10 percent of school children participate in the school breakfast program, targeted toward poor children, and about 60 percent participate in the school lunch program, available to all students.

According to the 600-page report, prepared by System Development Corp. of Santa Monica, Calif., several of the nutrients provided by the lunch program, including vitamins A and B6, calcium and magnesium, are "typically deficient in the diet of the school-age population."

The study also noted that "the biggest single determinant of School Lunch Program participation is meal price." It added that "contrary to some speculation, families in general do not reduce their food expenditures when their children receive subsidized meals at school." Both lunch and breakfast programs, the report said, tend to supplement a family's food supply, not its income.

Between the 1980-81 and 1981-82 school years, when eligibility requirements were tightened and the average price of the lunches raised, USDA internal reports showed that about 3 million students dropped out of the program. In the past year, participation has stabilized at 23 million students, according to a department news release accompanying the new study.

All lunches served under the program are subsidized, but last year students not meeting income eligibility criteria paid an average of 80 cents for their lunches.

Among the other findings in the report:

* School breakfasts served under the USDA program provide less vitamin A and B6 and less iron than breakfasts eaten by other children in the study, but more milk-related nutrients.

* As a result of the program cutbacks enacted in 1981, students in families with per capita incomes of $2,500 to $4,250 "received a much greater reduction in school lunch benefits than the general population" of students eating lunches. Participation among students in families with less than $2,500 per capita income was not reduced significantly.

* High school students who had been receiving free lunches were most likely to drop out of the program entirely if, due to eligibility changes, they were charged for the food.

In a news release accompanying the report, Assistant Agriculture Secretary Mary C. Jarratt said, "The report finds the national school lunch program is effective in safeguarding the health of the nation's school children by providing nutritious foods."