Park and recreation programs in Prince George's County will face cuts next year, while the Montgomery County park system will operate mostly at this year's level if budgets recently proposed by the bicounty Maryland National Capital Park and Planning Commission are approved.

In Prince George's, the program cuts will be necessary even though the proposed $26.8 million operating budget is 5 percent higher than last year's budget. Inflation, energy costs and salary increases will raise costs more than 5 percent.

In Montgomery, the proposed $25.4 million budget is $2.2 million or 9.5 percent higher, and would require a one-fourth of a cent increase in the county's park tax rate.

Increases in property values during the past year -- about 4 percent in Prince George's and 6.7 percent in Montgomery -- will bring both counties greater tax revenues at existing park tax rates, but not enough to offset inflation, according to the planning commission's budget document.

Prince George's plans to keep the same park tax rate, 40.42 cents per $100 of assessed value on a residence. Montgomery is proposing a small, one-fourth of a cent increase from its present 31.1 cent per $100 rate. The park tax rate is higher in Prince George's because the county funds all recreation programs from the tax, while Montgomery recreation programs are funded separately, from general county revenues. Both park taxes are tacked onto regular county property taxes.

Prince George's proposes increased charges at many of its parks to help counter the costs of inflation, including higher fees for the indoor-outdoor tennis courts at Watkins and Cosca regional parks, higher dumping rates at the Sandy Hill sanitary landfill and higher airplane repair rates at College Park Airport. The Old Maryland Farm at Watkins Regional Park, which was closed in September, will not be reopened, and maintenance and repair projects at county parks will be cut back.

In Montgomery, no significant changes in park programs are planned unless the County Council cuts the proposed planning commission budget. Significant cuts would have to be made if the park budget is kept at this year's level or is cut $1.1 million -- as recommended by the county executive, who has urged county agencies to reduce their 1982 budgets to 90 percent of this year's budgets.

If no increase is allowed, Montgomery would have to defer for at least a year the opening of the new Martin Luther King Jr. park in the eastern part of the county, significantly reduce maintenance and repair at other parks, and defer a number of minor projects, according to Montgomery Planning Board spokesman John Hoover.

And if "the 90 percent guideline" is followed, Hoover said, at least 24 park employes would have to be fired, overtime for park police would be ended and night operation of many parks would cease. Because the planning commission has been cutting its staff and programs since 1976, when it began a rigorous program of fiscal restraint, "There is nothing left to cut," said Royce Hanson, who leaves his post tomorrow after a decade as head of the Montgomery Planning Board, the Montgomery half of the bicounty planning commission. The present Montgomery park tax rate is below the 1976 rate, he pointed out. The proposed park budgets include a 6 percent pay increase for employes in both counties, plus merit increases that average 2 1/2 percent. Hoover said not only would the proposed increases be well below the increase in the cost of living in the Washington area, but "last year park and planning employes got raises below those of all other county agencies."

The two county councils will begin considering the budgets this spring and will act on the park tax rates in May.

In outlining the proposed Prince George's cuts, budget manager Douglas R. Sherwood said, "We're cutting back marginally, and we expect no grand cuts in 1982, although there probably will have to be in 1983" if the County Council allows no increase in the parks' budget.

At the last minute last May, the Prince George's council restored $1.3 million it had cut from the parks' budget, and to fund it allowed a 2-cent increase in the park tax rate, to 40.42 cents per $100 of assessed valuation.

The Old Maryland Farm, proposed for elimination this summer, was scheduled for closing last summer until the council provided limited funds to operate it until September. The on-loan cows, pigs and other barnyard animals were returned to their owners last fall, and the former year-round farm has since been closed. About 50,000 persons visited the farm last summer, according to Prince George's officials.

Three other model farms are operated by the National Park Service in the Washington area, although the Park Service this month announced preliminary plans to close one -- Turkey Run Farm in McLean. The other two are in Prince George's County -- the Oxon Hill Children's Farm and National Colonial Farm in Piscataway Park.

The higher charges planned include a $2 increase in the $9-a-ton dumping rate at the park system's Sandy Hill landfill and a 50 cents to $1-an-hour increases in tennis court rates. All the county's $210 tennis courts are free, except for the nine lighted indoor-outdoor courts at Watkins and Cosca parks.

The historic College Park Airport, operated by the planning commission, is expected to lose $44,000 this year. The commission proposes increasing its mechanical repair capacity for planes and charging higher rates, and is considering opening a concessioner-operated restaurant at the airport to help make it self-supporting.