In their own dignified fashion, the nation's public and private colleges are locked in a tug-of-war, with the American college student of the 1980s as the prize.

The latest round in this continuing struggle involves the seemingly neutral question of how much money the federal government should give to the needy student, Congress is trying to decide whether the ceiling on federal student grants should go up from 50 percent of a student's education costs to 70 percent.

In the complicated world of education politics, however that decision could spell doom to hard-pressed private colleges faced with the prospect of dwindling enrollments during the coming decade.

Under a House version of the student aid plan, the maximum federal grant for a student would rise from $1,800 to $2,520 over the next five years, with a provision that whatever the dollar amount the award cannot go over 70 percent of the student's education expenses.

The nation's state college systems have happily supported the House plan, which was passed last November. Student expenses at public colleges average about $1,500 annually, compared with a $5,400 average annual expense to attend private colleges.

On the other side of the fight has been the National Association of Independent Colleges and Universities, representing about 800 schools. Until recently the group has opposed raising the ceiling to 70 percent of expenses. The private colleges contend that under the House plan their students would get proportionately less than their public school counterparts.

Translated into education politics, the private colleges fear that their students, faced with larger out-of-pocket expenses after they get their federal grants, will begin transferring to public colleges where after-grant expenses would be smaller.

"That concerns us," said John Phillips, head of the independent college group. "It is absolutely essential these days to maintain competition in the educational marketplace."

Despite uneasiness on the part of the independents, Phillips and the group's leadership endorsed the House plan last summer. The group split, however, with about 150 of its members headed by Paul Hardin, president of Drew University in New Jersey, opposing the raised ceiling.

At the independent colleges' annual convention here this week, House and Senate members warned that opposition to the House plan could bring cuts in some $480 million in supplemental grants that are part of the House program and generally favor private colleges.

The group voted unanimously yesterday to support the House plan. After the vote, Hardin said his group would support the program unless the Senate cuts the supplemental grants.