The strangest Air Force bomber debate since 1921, when Billy Mitchell sank old battleships to prove the effectiveness of dropping bombs from airplanes, is about to unfold in Congress -- with tens of billions of dollars at stake.

The choice is between the bomber almost everyone in Congress knows about, Rockwell International Corp.'s B1, and the bomber almost no one in Congress knows about, Northrop Corp.'s "Stealth."

The immediate question for lawmakers is whether the B1 production line should be shut down, as the Air Force has promised, after the 100th bomber is delivered in 1988, or whether more B1s should be ordered, as Rockwell has begun urging in an intense lobbying campaign.

Northrop, which has staked much of its future on the supersecret Stealth, has been ardently arguing its case in what is shaping up as one of the year's preeminent dogfights on Capitol Hill. Northrop believes the government should stick to its plan of building only 100 B1s before buying 132 Advanced Technology Bombers (ATBs), as Stealth is formally known.

Now under development in California, Stealth supposedly incorporates new technology that makes it virtually invisible to enemy radar. But, because the program is so secret, even photographs of Stealth prototypes are forbidden and promoters are muzzled when it comes to singing the plane's praises.

Advocates contend that Stealth will be able to evade Soviet air defenses of the 1990s and perhaps beyond. Critics say the bomber threatens to be unstable in flight and is so small that it can carry little fuel compared with the B1 and thus would require more frequent in-flight refueling for long missions.

Besides the peculiarity of having one bomber visible and the other invisible in the public debate, the two parent companies insist that they are virtually powerless to influence the discussion.

"I go see a senator to try to persuade him to buy more B1s," said Bastian (Buz) Hello, head of Rockwell's Washington office, "and what do I tell him? I can't make a comparison with the ATB because I'm not allowed to know anything about it or discuss it if I did."

A Northrop executive who, in keeping with the stealthy nature of the debate, declined to be identified by name, sounded equally plaintive. "There's no fight. We're the empty chair. We can't say anything about our product because it's all secret."

Nevertheless, such obstacles have not stopped both contestants from hiring people with strong congressional connections to boost their cause. Robert Andrews, former aide to B1 enthusiast Sen. John Glenn (D-Ohio), heads Rockwell's lobbying effort. Northrop has hired a number of consultants, including former representative Jack Edwards (R-Ala.), who had been ranking Republican on the House Appropriations subcommittee on defense.

Yet another strange feature of the bomber war is that the Defense Department will not tell the public what it will cost to build 132 Stealth bombers. The Pentagon recently sent a cost estimate to the House Armed Services Committee but classified it top secret. Informed sources said the estimate is about $40 billion in fiscal 1981 dollars for the 132 Stealths compared with about $21 billion for the 100 B1s. Other sources put Stealth at $620 million per plane, or more than $80 billion for the entire program. Critics say both bombers could end up costing more than these estimates.

The battle is beginning to break into public view. In a letter to President Reagan urging the production of 50 more B1s, Rep. Robert K. Dornan (R-Calif.) and seven other House Republicans called the B1 "the eagle in hand" that should not be traded for Stealth, presumably the proverbial bird in the bush.

But Sen. Sam Nunn (D-Ga.), senior Democrat on the Senate Armed Services Committee, countered, "I would adamantly oppose any effort to continue production of the B1 beyond 100 bombers." Nunn said Stealth is in "good shape" and will be capable of penetrating Soviet defenses much better than the B1.

Rep. Mike Synar (D-Okla.), who said the administration's Stealth cost estimate is too low, is pushing for public disclosure of B1 and Stealth comparisons.

In previous bomber debates, such as whether to build the B70 in the 1960s or the B1 in the 1970s, Air Force witnesses presented charts, movies, slides and innumerable thick reports on cost and performance during extensive public hearings by congressional committees. This time, Stealth is so secret it is not even listed in the public version of the federal budget.

When Synar tried to see the Stealth at Northrop's plant, the Pentagon initially blocked his visit, then said he could go only if he obtained a permission slip from Rep. Les Aspin (D-Wis.), chairman of the House Armed Services Committee. That done, the Pentagon then insisted that Rep. William L. Dickinson (R-Ala.), ranking Republican on Armed Services, also sign off on the visit, Synar said.

Synar replied with expletives and thundered, "I don't need a Republican to clear my visit to a defense plant." The Pentagon relented. Upon his arrival at the California plant, Synar said, Northrop lobbied him on the program and provided a peek at what the plane will look like. Although neither he nor anyone else is allowed to describe the Stealth bomber, informed sources said it is shaped like a sting ray, a flying wing without the usual tube-like fuselage, to present few reflecting surfaces to searching radars.

"They had put up this big chart which showed all the states where Stealth work was being done," Synar said.

Similarly, Rockwell's lobbying campaign includes kits showing that practically every congressional district in the country has some kind of B1 contract or subcontract. Many workers at the B1 plant in Tulsa live in Synar's district, but he said he has not made up his mind on whether more than 100 B1s should be built.

Because his competitor's plane has been kept under wraps from all but a handful of decision-makers, Rockwell's Hello said, "This is the strangest debate over any kind of airplane I've ever seen.

"Every once in a while I say to myself, 'Let's suit up and put the gloves on.' And then I have to ask: 'To do what?' All we can do to advertise our product in sessions like this is to flip through these charts and show how well the B1 program has gone and how superior this bomber is to the B52," he added, noting that the venerable B52 is no longer the competition.

Hello acknowledges that if he and the other 10 Rockwell lobbyists cannot persuade Congress this year to keep the B1 in production beyond 1988, the program is probably dead. He argues that this would cost 20,000 jobs at Rockwell facilities in Oklahoma, Ohio and California.

Northrop executives also complain that the Stealth secrecy gag prevents them from rebutting allegations about their bomber, including assertions that the plane is running beyond cost projections and is plagued with stability problems. However, Northrop has kept one piece of firepower in reserve: the company's chief executive, Thomas V. Jones, is an old friend of Reagan's.