Republicans and Democrats in Fairfax County's sprawling 34th Senate District agree on one thing: The Senate race there this fall is a contest between an experienced candidate and an inexperienced one.

The trouble is, they don't agree on which is which.

Democrat Emilie Miller, a 47-year-old civic activist and former chairman of the County Democratic Committee, is missing no opportunity to tell voters about her three years' experience as legislative aide to retiring State Sen. Adelard L. Brault, whose shoes she hopes to fill.

"I've worked in Richmond," she says. "I know those people. I know how to get a bill through."

On the Republican side is John W. Russell, a 60-year-old retired federal defense planner who insists that his seven years as Fairfax City's mayor makes him--not Miller--the more experienced candidate.. He says of Miller's claims: "That's like me saying I could be secretary of defense because I've been in the Pentagon. There's a big difference between being on the firing line and being in the audience."

As they battle in one of the state's most sharply contested races for control of Northern Virginia's only open Senate seat, Russell and Miller have been struggling over many of the familiar themes that are proved vote-getters in Fairfax: transportation, education and human services.

A bigger question, however, is an intangible one: Can Brault anoint his successor? The diminutive Brault, a popular legislator and former Senate majority leader, has represented the district for about 18 years and is widely regarded as Northern Virginia's most influential representative in the General Assembly.

Miller has been making every effort to capitalize on her old boss' reputation, appearing at his side at fund-raisers, making him her campaign chairman and printing his name prominently on her campaign literature. A recent two-page press release from the Miller campaign carried Brault's name nine times.

Nor is Brault's the only assistance Miller has been receiving. Gov. Charles S. Robb paid a campaign visit last week, hailing Miller as a political insider who "knows how the system works." She has also received endorsements from the AFL-CIO, the Northern Virginia Board of Realtors and the area's teacher organizations.

Russell, by contrast, plans no campaign visits by prominent Republicans and says he isn't much worried about Robb's participation in the Miller campaign. "That was just the governor shaking hands," he shrugs. "He's running for vice president, you know."

For Russell, this year's race will be a duel of shoe-leather and stamps. He plans to walk through at least half the precincts in the district, which stretches from Springfield to Vienna and incorporates Fairfax City and Falls Church. Those he cannot reach on foot will receive campaign mailouts. The whole effort will cost between $35,000 and $40,000, by his estimate, or slightly more than the $32,000 Miller has set as her top budget figure.

Russell's campaign literature lists positions on a host of issues--he supports the state's right-to-work statute, stricter anticrime laws, and a balanced budget amendment--and he used that literature at a candidates' forum last week to launch his attack on his opponent.

"Look at these cards," he commanded, holding one of his own next to a Miller campaign card that highlighted her experience as chairman of the local Community Service Board and her recognition as a "woman of achievement" by the County Board of Supervisors last year. "This one Russell's tells you positions. This one Miller's doesn't tell you anything," Russell said. "Don't you think a candidate should tell you where they stand?"

Miller fumes at suggestions that she hasn't taken any stands, and says that Russell's acerbic manner has been a hallmark of his campaign. During a preprimary debate last spring, Russell responded to a question about the Equal Rights Amendment with a remark about not wanting to see women equipped with submachine guns because "they're dangerous enough without it."

Russell, an angular man who is described by friends as a "good old boy," now insists that the comment was a joke and says it has done nothing to jeopardize his support. But Miller, a staunch supporter of the ERA, says she sees nothing funny about it. "It's far too serious to make jokes about," says Miller, who hands out news accounts of the remark with her campaign literature. "Women are appalled."

For her part, Miller is stressing her support for a "balanced" transportation system that would include greater highway funding for Fairfax and completion of the 101-mile Metrorail system; merit pay for teachers and a state high-technology educational center located in Northern Virginia.

"I feel very confident of winning," Miller says, "because I have all the right issues and all the right credentials and the support of Brault and the governor."