An elaborate and delicate compromise aimed at ending the 75-year-old battle between Virginia's cities and counties over annexation came apart yesterday in the House of Delegates Appropriations Committee.

By a 11-to-8 vote, the committee decided to hold over until the 1979 session the money bill that has been described as the keystone of the agreement. The bill which would cost more than $100 million a year by 1982, would have given the cities more state aid exchange for their losing the right to try to annex parts on neighboring counties.

The committee may decide to reconsider later this week, but if the bill is resurrected, its future on the House floor is considered uncertain.

The counties have been under annexation pressure because the cities have been trying to recapture tax revenue lost when residents migrate to the suburbs. As the cities have had to provide increasing services while their tax base has shrunk, the pressure has intensified and relations between localities has worsened.

As opposition to the compromise designed to end the annexation controversy began to well up yesterday during debate, Del. Thomas J. Michie (D-Charlottesville), chief architect of the proposed agreement, pleaded: "We've got to look at the state as a whole and try to do what's right for everybody."

But rural legislators complained that the money bill shortchanged their areas by channeling most of the aid to urban areas in the form of law-enforcement funds. There was even opposition from legislators representing urban areas that would stand to benefit from the aid formulad. Where would the money come from? they asked.

The so-called "Micchie package" has been ranked among the most important legislation to be taken up by this session of the General Assembly. The legislature has repeatedly failed in past sessions to find a compromise that would bring cities and counties together.

Last year then-Gov. Mills E. Godwin urged the warring factions to compose their differences and bring a compromise to the General Assembly that could be written into law. Early in this session, the Virginia Muncipal League (spokesman for the cities) and the Virginia Association of Counties announced that they were finished battling and produced a compromise.

The Michie package, which had already been written, was hastily amended to incorporate elements of the compromise not already in one bil or another.

Two parts of the three-bill Michie package have already passed the House and gone to Senate committees, leading supporters to think that this was their year. But the money bill didn't move out of House Appropriations as fast as the other two bills advanced to the House floor.

When Michie, whose face was worn and tired from meeting after meeting, was asked wht he would do if the money bill didn't pass, he replied with gallows humor, "I think I would slit my throat.

After yeaterday's 11-to-7 vote against sending Michie at first tried to walk away from reporters who surrounded him. Finding himself trapped in the hallway, he relented for an improptu press conference.

"I'm disapponted," he said, "We will look into an amendment to meet the objections concerning police aid."

It was the formula for providing law-enforcement funds to localities that put the money bill in troublw in Appropriations, and caused even more sponsors to decide not to report it to the House floor.

Of the following $48.3 million in extra stare aid that would go to localities in 1980, almost $33.4 million would be for law enforcement. Because rural counties already have their law enforcement largely paid by the state, they would not get any extra money under the bill, while millions in additional aid would go to both cities and urban counties.