One afternoon last week, Thomas Dine decided to make the two-block trip to Capitol Hill for a battlefront reading on progress of the administration's proposed arms sale to Saudi Arabia.

Dine, who as director of the American Israel Public Affairs Committee (AIPAC) makes him the point man for the nation's so-called "Jewish lobby," wound up paying calls on 11 senators before the day was out, as he rattled off his case against the sale.

Even by standards of AIPAC, long considered one of the most aggressive lobbies on the Hill, it was an impressive day's work.

And it stood out all the more because Dine's opposite number in the Saudi lobby, Frederick Dutton, has been a virtual stranger on the Hill these past few months. A onetime aide to both John and Robert Kennedy, Dutton claims he has spoken to one senator about the arms deal, "and that's only because he absolutely, positively insisted on doing it."

The contrasting styles of the lobbyists on the Airborne Warning and Control System (AWACS) plane issue spring from the different strategic calculations of the parties they represent.

The Saudis are determined to take their place on the sidelines while they watch the Reagan administration navigate the package through Congress. The royal family did dispatch a special representative to town a month ago, but with careful instructions, according to a Saudi spokeman, not to speak above a whisper.

Prince Bandar bin Sultan, an English-educated, American-trained pilot, is here "primarily to answer technical and military questions on the sale," in the words of Crawford Cooke, the public relations consultant whose firm has a $470,000 contract with the Saudis.

Bandar, who doesn't speak to the press for attribution, has been meeting congressmen in their offices, hosting parties at his elegant townhouse in Kalorama or his six-room suite at the Fairfax Hotel and, when called upon, sitting in on administration strategy sessions.

The resolutely low-key approach of the Saudis has been shaped by their belief that having to lobby for the sale themselves would defeat part of the rationale for the purchase.

"One of the things the Saudis want is to find out just how credible is the U.S.-Saudi relationship," Dutton said. "They want to know how reliable our government is in a crunch, and they take the position that this is a battle for the administration to fight, not them."

At a retainer of $200,000 a year from the Saudi government, Dutton is hardly in a position to question the judgment of his clients. Yet he finds himself wondering if he could have been more effective these past few months had he been allowed to take the muzzle off.

"We're in a tough, uphill situation right now," he said of prospects for the package. "If I had my way, I'd have bumper stickers plastered all over town that say 'Reagan or Begin,' " an effort to exploit what he perceives as widespread resentment of the idea that a foreign chief of state could exercise a kind of veto over presidential decision-making.

"That kind of stuff really plays in Peoria," said Dutton, a ringwise former campaign manager to Robert Kennedy and California Gov. Pat Brown. "But people in this country just don't understand the Arab mind. Desert Arabs like the Saudis are cool, low-key, laid-back. They don't want to have to make the case for this. I was far more aggressive in 1978 in lobbying in support of the sale of F15s to Saudi Arabia and the word came back that my approach didn't play so well in Riyadh."

Dutton is hoping that the Saudi art of gentle persuasion will stand up well in contrast to the approach of the pro-Israel lobby, which he characterizes as heavy-handed. "AIPAC," he said, "just doesn't know how to easy-does-it."

His charge is one that crops up in one form or another whenever the so-called Jewish lobby is thrust into center stage, and it has left the AIPAC lobbyists a bit wary. On matters relating to his organization's lobbying techniques, Dine and others in his shop declined to be interviewed for the record.

His organization is the lobbying arm of a community known for its high levels of education and political activism and its deep support for the Jewish homeland. AIPAC has a budget of $1.3 million, a staff of 30 and a membership of 12,000. The presidents of the 35 major Jewish organizations from around the nation sit on its board, and through their contacts, AIPAC's fountain of research material reaches a readership estimated at 200,000 people.

By the testimony of Dutton, AIPAC is the the "most muscular lobby in the country; it makes organized labor and business look like peanuts." Jewish leaders invariably wince when they hear chacterizations like that. They view them as one part compliment and 99 parts gamesmanship.

"Puffing up the importance of the Jewish lobby is a big part of what the Arab lobby is all about," said one source in the Jewish community. "It's just a code for saying that if you don't watch out, the Jews'll take over."

Jewish leaders say the source of their lobbying muscle grows out of nothing more complicated than the grass-roots activism of the people they represent. "You can send out a mailgram to 10 key Jewish leaders from a state like Iowa and know that, the next day, eight or nine of them are going to be on the phone with their congressmen," one lobbyist said.

"It isn't that Jews do anything different or better than other lobbyists, it's just that our grass-roots support is much stronger."

As to the argument that Jewish groups overstay their welcome by flooding too many congressmen too many times with too many letters, telegrams and phone calls, another leader noted:

"We are assertive, we have direction, we know what our objectives are and where the resistance lies. Some people will think we are overbearing, that we're too much in presence, but with that comes a certain amount of respect. To do it any other way would mean not getting the job done."

That out-front, unapologetic aggressiveness is a trait that not all in the Arab world recoil from. Indeed, despite the reticence of the Saudis in the AWACS fight, the association that has been lobbying for all Arabs in this country for the past decade has been borrowing the AIPAC style, right down to the typography on their newletters, as it brings pressure to bear on Congress.

David Sadd, director of the National Association of Arab Americans (NAAA), shares the Saudi belief that the principal job of selling the AWACS package belongs to the White House. But he is openly critical of the Reagan administration's effort so far, taking special aim at national security adviser Richard V. Allen. "Many in the Arab community see him as a principal Israeli plant within the White House," Sadd said.

Sadd, an investment banker by training, believes the economic benefits that will flow to the United States from deepening its ties to Saudi Arabia constitute a powerful, but as yet untold, argument in favor of the sale.

In order to try to get the story out, Sadd has been in touch with the corporations that have large chunks of the $7 billion in trade this country does each year with Saudi Arabia.

"We're encouraging them and their employes to put some pressure on," he said. Sadd has met with more exasperation than successs. His group did a study of political action committee contributions made to congressmen by 30 corporations that do business with the Arabs. And he was chagrined to discover there was "absolutely no correlation" to the Middle East voting record of the recipients.

"We've pointed this out to the CEOs chief executive officers of the corporations and they seem surprised themselves," he said. His group is putting together a familiar interest group tool, a rating system for congressional votes, so the corporations will have better information in the future.

In its efforts to match swords with AIPAC, the Arab lobby faces certain obvious drawbacks. It starts with a constituent base that is smaller (estimates of the American Arab population range from 1 million to 2 million; there are about 6 million Jews in America), more fractured (the war between Lebanon and Syria has strained relations within NAAA), and one that does not share the historic zeal of the Jews for political activism in this country.

Like Dutton, though, Sadd is hoping that the zeal and potency of the Israel lobby will eventually be its undoing. "If the AWACS sale gets blocked, then the monkey's really on their back," he said, predicting a backlash against Israel and the Jews.

As they sense that victory in within grasp on the AWACS issue, Jewish leaders themselves are spending some time worrying about the cost of winning. "In the last 10 days, it's almost become a cliche that if we lose we lose and if we win we lose," said Hyman Bookbinder of the American Jewish Committee, the elder statesman of Jewish lobbyists in town.

"It's a silly cliche," he said. "We'd all prefer not to have to be in this fight, but once we're in it, believe me, winning is winning."