A slightly revised version of President Carter's proposal to expand the government's college tuition grant program won formal approval yesterday in a House Education and Labor subcommittee, paving the way for action by the full committee next week.

The legislation, which was approved by unanimous vote. would provide somewhat larger tuition grants than Carter proposed for middle-income families and would eliminate the president's proposal to limit student-loan guarantees to families earning $40,000 or less.

However, in deference to White House budgetary warnings, the panel voted to give the House a choice between a financing level that would hold to Carter's $1.2 billion ceiling on extra costs and a more generous version that would add $200 million.

The more costly version would allow larger grants to students in all income brackets and extend at least some scholarship aid to those whose families earn up to $25,000. The grants provided in the less expensive measure would go only to those whose families earn $23,440 or less.

Except for the choice in how costly the program should be, the subcommittee bill is virtually identical to one approved Friday by the Senate Human Resources Committee. The administration essentially has endorsed that bill.

THe Senate bill is in a race to the floor with a rival tuition tax credit proposal approved earlier by the Senate Finance Committee. In addition to college expenses, that bill would cover expenses for private and parochial elementary and secondary schools.

Carter lambasted the tax credit proposal again yesterday in a message on aid to education. He proposed the increase in federal scholarship money almost solely to head off enactment of the tax credit plan, which he says would be wasteful and too costly.

Like the Senate committee the House panel also voted modest increases in the work-study grant program and the supplemental educational opportunity grant program for needy student.

The cost increases approved by the subcommittee yesterday would range from $1.2 billion to $1.4 billion over existing levels, depending on which version is accepted, compared to $1.4 billion for the Senate measure. Carter has sought to hold the increase to$1.2 billion.