They are Washington's glamorous counties, natural competitors for new business and prestige, rich, prosperous and growing.

But during the past decade Fairfax and Montgomery counties have grown in different ways -- Fairfax, fast, and Montgomery, slowly. The result, a new study concludes, has been sharp differences between the two counties in who pays the tax bill and a resurgence of long-debated, but unsettled questions about Fairfax County's failure--and inability--to control its own growth.

The study by the Washington-based Urban Institute was commissioned by the Fairfax Board of Supervisors last year. Since a preliminary draft was released this summer, it has drawn heavy fire from the county's influential business community and from some supervisors who question its conclusions.

That criticism is not surprising given the study's main conclusion: Fairfax homeowners pay a bigger chunk of the county tax bill than Montgomery homeowners and yet receive less in per capita spending for schools, police, fire, libraries and parks. The gap between the two counties, the study concludes, is a product of Fairfax's residential housing boom and its comparatively moderate commercial/industrial growth.

Population in Fairfax grew by more than 30 percent in the last decade, to 596,901 people in 1980 from 454,275 in 1970. That growth was three times more than Montgomery's, which went to 579,053 in 1980 from 522,809 in 1970. At the same time, the study argues, Fairfax homeowners were paying a bigger portion of the tax base than those in Montgomery, as residential growth outstripped commercial/industrial growth in Fairfax. Among the Urban Institute's conclusions:

* While the per capita costs to taxpayers of the school system in Fairfax were 12 pecent higher than in Montgomery in 1981, Fairfax's school spending per pupil is 10 percent lower than Montgomery's.

* Rapid residential construction in Fairfax led to a lower percentage of the county's real estate tax base being paid by commercial and industrial properties--and a higher portion paid by the homeowners.

* Fairfax could have saved more than $31 million in 1980 alone if it had grown more slowly and its school enrollment had dropped significantly through the 1970s as Montgomery's did.

When the report's author, Thomas J. Muller, appeared before the Fairfax Board to discuss his findings, he received mixed, if cordial, reviews from the supervisors, all of whom will be up for election in 1983.

Board Chairman John F. Herrity, a Republican who has been considered a supporter of the county's development community, blasted the report for failing to consider whether any income has been generated by residential growth. Muller acknowledged that his report had not considered the net financial effect of growth on the county, but maintained that even if it had, the thrust of his conclusions would not differ significantly.

"This study sort of reminds me of examining a corporate profit-and-loss statement without looking at the income side, just looking at the expense side," Herrity said.

"If you take a corporate profit-and-loss statement and look at the expense side and say, 'We're not going to look at the income,' I don't think any CPA or audit firm would accept that as a viable financial document."

Still, debate on the issue continues to simmer, bubbling up in veiled and not-so-veiled references at County Board meetings. The recent release of the Urban Institute's final report may revive the debate. The Fairfax Chamber of Commerce was so troubled by the institute report that it produced its own counter-report--a public opinion poll indicating that most county residents support a continuation of the current policy of "orderly" growth.

"Intellectually dishonest," is how James M. Rees, president of the Fairfax chamber, dismissed the study. "It's such a small snapshot of the total picture. Development and growth are very complex issues. You just can't say it costs a lot of money to build houses. The real question is what do you do about that?"

Just what to do about growth has indeed been the central issue confronting Fairfax for much of two decades. That's how long the county has grappled with the question of how to slow residential growth.

But today it is apparent that the county has failed to control its growth. It has, as critics have said, proven impossible to legislate the rate of growth, mainly because Virginia law and court decisions have severely limited local land-use planning.

What's more, despite an aggressive and largely successful county campaign to lure new businesses, Fairfax is still likely to attract more new residents this decade than any other county in the Washington metropolitan area, according to county planners.

Montgomery, by contrast, has been far more successful in its planning efforts. With sympathetic courts to fall back on and a tradition of planning going back to the 1920s, Montgomery is the envy of the so-called "slow-growthers" in Fairfax. The inevitable comparisons of the area's two wealthiest counties--Montgomery's $15,641 per capita income ranks sixth in the nation and Fairfax's $13,403 ranks 19th--especially rankle Herrity.

"What makes me want to head for the nearest door . . . is every time I turn around somebody is saying how great Montgomery County is," he said. He said Fairfax's residential growth is, for the most part, beyond the control of county politicians.

The debate on growth in Fairfax has ricocheted from courtroom to County Board room and back since the late 1950s. One of the county's main obstacles to regulating its growth through legislation was the Dillon Rule in Virginia, which prohibits localities from passing laws without specific enabling legislation from the state. Moreover, Virginia courts have repeatedly ruled in favor of the rights of private landowners over the ability of government to promote social goals. The result was a steady stream of county schemes to thwart fast growth that were slapped down by the state courts.

From the precedent-setting Carper case in 1959, in which the Virginia Supreme Court squelched the county's attempts to slow growth in the western two-thirds of the county, to a series of sewer and tax cases in the mid-1970s, the state courts repeatedly stopped the county's slow-growth efforts. The plaintiffs--and victors--in most of the cases were Fairfax developers.

Still, the slow-growth advocates did not give up. The slow-growth board of 1972-76 tried a host of growth-stunting approaches--including sewer moratoriums, an emergency ordinance to halt all development in the county for 18 months, and an unstated policy to defer all controversial rezoning applications indefinitely--to no avail.

"I guess almost every method to control growth that's conceivable to mankind was attempted," Herrity said, "most of which was thrown out of court. We have recognized our limited legal ability."

"I've heard that we've tried it all before," said Annandale Supervisor Audrey Moore, a Democratic maverick who has opposed rapid residential growth and whose research originally spurred the board to commission the Urban Institute study. "The problem is that we didn't try it all before. Contrary to popular developer mythology, Fairfax is very much in control of its own destiny."

Moore maintains that the county should extract more concessions from developers eager to build in Fairfax, such as gutters, schools and roads.

Herrity and his allies respond that state law does not allow Fairfax to require such concessions, and that they would only boost the cost to those seeking homes in the county.

In what may lead to the newest challenge to growth in Fairfax County, the supervisors last month voted to restrict development in the western quadrant of the county, known as the Occoquan Basin.

The board decided to restrict building there to one home for every five acres to limit possible pollution to the area watershed that provides water to 600,000 Northern Virginians.

But many of the supervisors acknowledged that the decision to limit the density of the Occoquan Basin could again lead to a flurry of lawsuits--again based on the rights of Virginia property owners. "We're going to get sued even if we float out of here on wings," quipped Herrity.

If the downzoning in the Occoquan Basin, known as the county's "last frontier," is successfully challenged, it may mean that controlled growth advocates in the county will have lost their battle once and for all.

Montgomery, in sharp contrast to Fairfax, imposed sewer moratoriums in the 1970s, which ensured that most of its population growth came from births rather than new families.

Maryland law also allowed Montgomery to require that subdivisions and other developments not be built unless adequate public facilities to serve them were in place.

Fairfax, Moore charges, has allowed developers to stick the county with millions of dollars in bills for roads, sewers, curbs, gutters and other facilities.

"Montgomery has had a consistent growth through the years," said Moore. "They're much more carerful than we are."

Perhaps the greatest impact of Fairfax's population boom in the 1970s was on the county's school enrollment.

While school populations around the country declined in the last decade, Fairfax school enrollment fell only 2 percent. Montgomery's school enrollment dropped 22 percent in the last decade.

Had Fairfax school enrollment dropped that fast, the Urban Institute report says, Fairfax would have saved $31.7 million in 1980.

Reviewing Fairfax's lower spending compared to Montgomery's for basic services such as police, fire department, libraries and parks, Moore concluded: "While spending money for government services is not necessarily a guide to how good those services are, it would appear that the public is being shortchanged."

Herrity bristles at the comparison: "Frankly, we have a lower crime rate, we have a lower unemployment rate and a better bond rating than Montgomery County. We must be doing something right."

One issue the supervisors do agree on is that Fairfax must increase its ratio of commercial and industrial taxpayers to residential ones to lighten the tax burden on residential taxpayers.

Officials in Fairfax say the gap is closing yearly as the county pursues new business, especially high technology firms, and the county's business tax base has been climbing steadily since 1979, when the current board was elected.