Candidates for Montgomery County executive, in their liveliest face-to-face debate of an otherwise quiet campaign, last night painted widely different pictures of the current state of the county, its economic health, crime problems and its fiscal management.

The sharpest disagreement between County Executive Charles W. Gilchrist and GOP challenger Joseph McGrath came over McGrath's proposal to cut back funding for the county's Office of State Affairs, Montgomery's lobbying arm in Annapolis. McGrath said the office could be made part time with a resultant saving of about $200,000. Gilchrist called such a proposal "a terrible mistake."

Throughout the debate, before an audience of about 50 persons at the Planning Board auditorium in Silver Spring, Gilchrist emphasized the record of his four years in office, repeatedly citing statistics and figures designed to support that record. He said the number of new housing units constructed in the county had increased during his term, more police officers were patroling the streets, the county had retained a AAA bond rating and Montgomery led the state in capital investment.

Gilchrist repeatedly accused McGrath of speaking in generalities, and he chided him to "give me specifics." At one point, after McGrath completed an answer, Gilchrist said that "we're talking in such incredible generalities here . . . . I really don't know what we're talking about."

McGrath, a former bank vice president making his first run for political office, painted a verbal picture of a county where property taxes have been increased frequently, where 15,000 persons are unemployed and which has attracted little economic development compared to other counties.

Near the close of the debate, which was sponsored by the Montgomery County Press Association, McGrath read a line from a report of the Merit System Protection Board, which concluded that the civil service system had been abused. "It's time for a restoration of competence, integrity and professionalism at the level of county executive," McGrath said, "and I intend to deliver that."

Neither candidate claimed a victory in the debate. Gilchrist's supporters, however, were clearly elated by the way their candidate repeatedly used specifics and statistics to state his case.

"I think Charlie showed himself to be the executive with a firm knowledge of the facts," said lawyer Gilbert B. Lessenco, Gilchrist's campaign chairman.

McGrath said that he believed he did offer specifics and that Gilchrist's assertions that he spoke only in generalities were "another smoke screen."