The two candidates for a seat on the Arlington County Board stood on the podium at a recent civic association meeting, tossing out remarkably similar answers to questions about taxes and development. Finally, a white-haired woman turned to her husband. "Look," she said in a stage whisper, "they're even dressed alike."

That observation, say officials of both parties, is what bothers them most about this race. Even Democrat John G. Milliken and Republican-backed independent Simone J. (Sim) Pace concede they agree on most issues -- and there are few in this campaign. As a result, political coattails may well determine which man will succeed outgoing board member John W. Purdy, a Democrat, after Tuesday's election.

"I hear over and over again that it's too bad we have to run two nice-looking young men who seem qualified and make a very good impression against each other," says Arlington Republican Party chairman Jade West.

"There are still a phenomenal number of undecided voters out there and we're trying to tell them that the bottom line on the ballot is important, too," adds West, whose party has made substantial gains in recent years in Virginia and in Arlington, which has the reputation as the state's most liberal jurisdiction.

Ann C. Broder, a veteran Democratic activist and Arlington school board member, says the lack of substantive issues in this race differs sharply from previous years when support for Metro or high property taxes were major concerns. "I think some people feel, 'They're both nice young men so why should I vote for one over the other?' I guess it'll depend on how people feel about the president," she says.

Many say Arlington's only local race also may hinge on how people regard incumbent Democratic Rep. Joseph L. Fisher, Milliken's political mentor who is running with his one-time congressional aide as a team. Fisher is, however, locked in a close race of his own with Republican Frank Wolf and the impact of the legislator's coattails are far from certain.

"What would hurt me and would hurt Joe Fisher is if substantial numbers of Democrats stayed home, but I don't think that will happen," observes Milliken, a 36-year-old Washington lawywe whose earnest manner and sandy-haired, pleasant appearance has won him the sobriquet "Boy Scout" in certain Republican circles. "We're running as a team and our support comes from the same base. But I don't think his fate for mine depends on the other."

Pace, 38, the darkly handsome vice president of Blue Cross of the District of Columbia, has suffered from a lack of name recognition and difficulty in raising funds, according to Republican officials. Campaign finance reports filed this week show that Pace has raised about $20,000 to Milliken's nearly $40,000.

Unlike Milliken, a former chairman of the Arlington Democratic Committee, Pace was plucked from political obscurity earlier this year by a Republican troika of county board members who won reelection last year and will control the board at least through 1983.

Arlington board members are elected at-large, serve four-year terms and are paid $9,000 a year for jobs that are considered part time. The current Republican-backed majority consists of chairman Walter L. Frankland Jr., vice chairman Stephen H. Detwiler, and Dorothy T. Grotos, Purdy and Ellen M. Bozman are endorsed by a Democratic coalition.

Trying to overcome the near-vacuum of issues, Pace has tried to link his opponent to a political force that has fallen from favor with voters: the non-partisan Arlingtonians for a Better County (ABC). In the past two years, Republicans, who have made large cuts in the property tax rate, have succeeded in tarring the 25-year-old ABC with a spendthrift image.

Although Milliken has been endorsed by the organization, Democrats hope to minimize that by having him run as a Democrat rather than as an independent with ABC and Democratic backing, as past candidates have done.

While Pace scores Milliken's ABC connections and tells voters that the Republicans have lowered property taxes "an incredible 22 percent" in the past two years. Milliken reminds constituents that the Republicans last year raised the water-sewer fee 33 percent and the trash collection fee 47 percent. He adds that, despite cuts in the tax rate, the average homeowner is paying higher taxes because assessments have risen so drastically.

Both men say they are concerned about controversial high-rise buildings recently approved by the county board despite the opposition of federal planning officials who say the structures will mar the Washington skyline.

"I distinguish myself sharply from the present development majority," says Milliken, who adds he would have voted against a recently approved 14-story office building planned for a site opposite the county courthouse. Pace says he would have preferred something shorter, but refused to say how he would have voted on the building.

Meanwhile, the preferences of a record number of newly registered voters are a question mark hanging over the entire race. Arlingtonians are notorious ticket-splitters -- they sent former Republican Rep. Joel T. Broyhill to Congress for 22 years while electing Democrats to a host of local offices -- but some Democrats fear the Republicans have mounted a strong and effective registration drive.