Fairfax County Supervisor James M. Scott's announcement that he will resign from the county board next month after 14 years in office has given both Democrats and Republicans something to prove.

Fairfax Democrats, buoyed by their success in last November's statewide elections and a special election in January to fill a vacant state legislative seat in Annandale, are eager to demonstrate that their new momentum is more than the product of Republican miscues.

The GOP, which emerged from a county convention last month badly divided, must show that the venom between the party's moderate and conservative factions has not poisoned its chances to win at the polls.

The special election to fill Democrat Scott's Providence District seat will be held July 15.

At first blush, even some Republicans concede, the Democrats may have a better chance at winning the seat on the nine-member county Board of Supervisors.

First, as the party with more to lose in the election, the Democrats are running scared.

If the Republicans take control of the seat, which Scott has won four times since 1971, they would increase their current 5-to-3 majority on the board by one. That would leave Democrats, who hope to regain control of the board in the 1987 general elections, at a nearly insurmountable disadvantage, and could ensure a Republican majority into the 1990s.

Second, the Democrats seem to be united behind a candidate, School Board member Kate Hanley, while Republicans seem divided between state Del. Stephen E. Gordy and Robert Beers, an aide to Supervisor Thomas M. Davis III. The two will go head to head at a party canvass May 27.

Finally, both GOP candidates have political drawbacks.

Beers, 38, an accountant who recently received a law degree, has not held elective office in Fairfax and is virtually unknown outside party circles. Several high-ranking Republicans, speaking privately, disparage his appearance (he is baldish), say they are not enthusiastic about his candidacy and doubt his ability to win. Nonetheless, Beers has been working diligently to round up supporters since Scott, who is also baldish, announced May 5 his plans to resign.

Although Gordy, a 66-year-old retired Army colonel and former school principal, is rated a better bet at the polls than Beers, he, too, is a political question mark. An amiable man with a knack for tripping over the English language, he is not known as a hard campaigner and was nearly defeated by a little-known Democratic challenger in last November's elections for the state House of Delegates.

"I'm the only one who's run and gotten voted on," he said in an interview after he announced his candidacy last week. "I would be appealable to the voters across the board."

Gordy, who was considering retiring from the legislature, was ranked near the bottom -- 98th out of 100 state delegates -- in terms of effectiveness in a Norfolk newspaper survey last year. He has little experience in local government.

"None of these people are ideal candidates, including Kate Hanley," said Davis, the Mason District supervisor. Davis, whose district abuts Providence inside the Beltway, said he supports Beers, his employe since 1980. ("The guy's been my aide for seven years," Davis said of Beers. "What kind of guy would I be if I didn't support him?")

Davis pointed out that Hanley was the only School Board member to vote against the fiscal 1987 school budget. Hanley said she voted against the budget because it did not include what she considered an adequate increase in salaries for teachers.

Voter turnout for the midsummer election is expected to be low. Campaign officials in both parties predict that as few as 8,000 people -- about a tenth the population of the district -- will show up to vote. Whichever candidate can get 5,000 votes seems certain to win.

That means that the election is unlikely to be a contest of ideas or personalities, but a tactical struggle that could depend on which party is more skilled at identifying its voters during the next eight weeks and producing them on election day.

At that, the Democrats may enjoy yet another edge: Unlike the Republicans, they are unified.

At the county Republican convention last month, the party's conservative faction was embittered when Benton K. Partin, a retired Air Force general, was ousted after four years as GOP chairman. Some conservatives vowed they would seek revenge on a coalition of elected officials that opposed Partin, which included Gordy.

County Republican leaders say the divisiveness of the convention is behind them, and that the party's internal problems will not play a part in the upcoming special election. If, as seems likely, Gordy is the Republican nominee in the Providence District supervisor's race, those assertions will be put to the test.