Next week, a wily Chicagoan and a maverick Oregonian will sit down at a congressional negotiating table to hammer out a sweeping rewrite of the nation's tax laws.

The personalities of House Ways and Means Committee Chairman Dan Rostenkowski (D-Ill.) and Senate Finance Committee Chairman Bob Packwood (R-Ore.) could hardly have less in common. Rostenkowski is a crafty vote-getter schooled in machine politics; Packwood, an eclectic philosopher with a streak of independence. They have little fondness for each other.

But as politicians, the chairmen are locked together whether they like it or not. Rostenkowski and Packwood share the goal of sending a tax bill to President Reagan's desk by Labor Day -- and the knowledge that their reputations will suffer should they fail.

"These guys have to get along, ultimately," said a former congressional aide who has watched both men. "They have to produce a bill. If their personal pique broke down the process, they would both look bad."

Already, the chairmen are close to a consensus that the final measure should give more tax relief to the middle class than the Senate bill does and cut tax rates for individuals more than does the House version.

So far, that framework has been laid out through the news media, with little direct communication between the two men. When Rostenkowski and Packwood have faced each other in the past, their encounters sometimes have been marked by conflict and insults.

In 1980, before either lawmaker headed his tax committee, Rostenkowski made a speech on the House floor complaining about a tax break for timber that Packwood had inserted in a nontax bill. He called it "another tax incentive of questionable value for an already favored industry."

In 1984, Packwood told Rostenkowski that he didn't know what he was talking about during a conference debate over a tax-free fringe benefit favored by Packwood. Rostenkowski, by then chairman of Ways and Means, maintained his opposition to the provision and Packwood was defeated.

In the waning days of the 1985 congressional session, Rostenkowski boycotted a conference committee on spending cuts because a fund to clean up toxic waste had been added to the bill by the Senate. Packwood scheduled a meeting anyway and, on his own, invited the House conferees, who supported Packwood's version of the fund. The unusual move led Rostenkowski to complain to Senate Majority Leader Robert J. Dole (R-Kan.).

Last month, Packwood refused to chair a conference committee on a minor water-resources bill. He said the issues in the bill were too unimportant to be resolved formally. But Rostenkowski's allies noted the move put Packwood in line for the chairmanship of the tax-bill conference, a position the chairmen of the tax-writing panels take turns holding.

After several more weeks of jostling, it appears Rostenkowski will chair the tax-bill conference.

"They're not friends. I don't think they're enemies either. They're both strong-willed. I think they'll do just fine," said William M. Diefenderfer, chief of staff of the Finance Committee.

Witnesses to past confrontations point out that relations between the two have improved since those incidents. Packwood apologized to Rostenkowski for setting the meeting on the toxic-waste fund, calling it a misunderstanding. The chairmen have spoken frequently as tax revision has progressed through Congress.

Even if Packwood and Rostenkowski bury what enmity might remain, the conference is likely to spotlight their divergent styles.

Rostenkowski, a granite-faced protege of the late Chicago mayor Richard Daley, plots the drafting of a piece of legislation in detail. When Ways and Means was debating tax overhaul last fall, for example, he decided in advance exactly how much revenue he could afford to give away in tax breaks and still reduce rates without increasing the ederal deficit.

"I had a plan," Rostenkowski said in an interview after the Senate passed its tax bill last month. "I on't know if Bob had a plan. If he did, you couldn't put it together. I had a column of figures on where we were, how much will this cost, how much we could afford to do."

The committee got off to a shaky start and overruled its chairman on some key votes, but recovered after Rostenkowski set up six-member "working groups" to settle controversial issues. The groups, headed by Rostenkowski loyalists, were made up of four Democrats and two Republicans. Rostenkowski tracked the progress of each group as members tried to balance the pain of ending tax breaks with the need to raise revenue to pay for reducing rates.

According to Rep. Marty Russo (D-Ill.), head of one group, Rostenkowski would slip into the room where the task force was meeting and watch its progress in silence for a while.

"Then he finally said, 'I can't give any more,' " Russo said. "He knew how much he wanted to lose. Nobody else did."

Packwood's approach to tax overhaul, on the other hand, might be characterized as erratic but innovative. The rumpled, mercurial senator first said of tax revision that, "I sort of like the tax code the way it is." Even after Packwood converted to the cause, the first rate-cutting bill he set before his committee retained many special breaks.

As that foundered, Packwood made a move a more traditional politician might have eschewed: He withdrew the measure and started again with a radical plan proposing a top tax rate for individuals of 25 percent and no deductions.

The momentum swung his way almost immediately, and Packwood steered a "core group" of six senators toward a revised version with a top rate of 27 percent. It cleared the committee, 20 to 0, and passed the Senate almost unchanged by a 97-to-3 vote.

"Bob Packwood is a hard charger. He just wants to get things done," said Sen. John C. Danforth (R-Mo.) as the bill neared approval by the Finance Committee in May. "There's a lot to be said for that approach. It's refreshing to see someone who wants to deal with the big issues in a bold fashion."

Sharing the stage with Rostenkowski and Packwood during the conference, expected to take several weeks, will be other powerful players with their own agendas. Dole, a former chairman of the Finance panel and a presidential hopeful, is expected to claim some popular issues, such as tax relief for the middle class. He also will seek to protect such home-state industries as oil and gas and private aircraft manufacturing.

Sen. Russell B. Long (D-La.), ranking Democrat on the committee and also former chairman, is retiring this year and thus will be under less pressure to bring tax benefits back home. Nonetheless, he can be expected to try quietly to protect tax breaks that let workers buy stock in their companies, favorable tax treatment for oil and gas and the deductibility of state sales taxes.

Sen. Lloyd Bentsen (D-Tex.), the second-ranking Democrat on the panel, will assume more importance than someone of his position might ordinarily command, because he will head the Finance Committee next year if the Democrats regain control of the Senate. His positions will be watched for clues of what a Bentsen chairmanship might be like.