For all their differences, President Biden and Prime Minister Rishi Sunak of Britain share a challenge: operating in the wake of a larger-than-life predecessor. They have tactics in common, too.LONDON — For years, Boris Johnson and Donald J. Trump were viewed as populist twins — flamboyant, scandal-scarred, norm-busting figures, acting in a trans-Atlantic political drama. With both out of office, at least for now, a more timely and intriguing comparison is between Prime Minister Rishi Sunak and President Biden.Though they differ by obvious metrics — young vs. old, conservative vs. liberal — Mr. Sunak and Mr. Biden are using strikingly similar methods to govern in the wake of their larger-than-life predecessors. Both have tried to let the steam out of their countries’ hothouse politics by making a virtue of being, well, a little boring.The similarities are more than stylistic: Both lead parties that are divided between centrist and more extreme forces, whether to the right, for Mr. Sunak, or the left, for the American president. And both are dogged by poor poll numbers, in part because of economic ills but also because their pragmatic, undramatic style can seem ill-suited to the polarized politics of post-Brexit Britain and post-Trump America.For Mr. Sunak, who took office in October amid an economic crisis and after months of political upheaval that left his Conservative Party exhausted and unpopular, Mr. Biden might offer a blueprint for political rehabilitation.Two years into his term, Mr. Biden has confounded the skeptics, with the Democratic Party performing unexpectedly well in the midterm elections, in defiance of historical trends that typically punish the party in power.“Boris and Trump were generalists, short on details and ideologically flexible, but the sheer force of their personality brought them to the top, and eventually led to their downfalls,” said Frank Luntz, an American political strategist and pollster who was a classmate of Mr. Johnson’s at Oxford University.“Rishi and Biden are the exact opposite,” Mr. Luntz continued. “Not particularly great communicators, quite often trapped in the weeds of details, but able to move their governments forward because of their detailed knowledge and experience.”President Biden and Jill Biden after returning from Camp David on Sunday.Pete Marovich for The New York TimesCircumstances forced both leaders to press for emergency legislation right off the bat: Mr. Biden, to cushion the damage caused by the coronavirus pandemic; Mr. Sunak, to counter the disastrous foray into trickle-down tax policy engineered by his immediate predecessor, Liz Truss. That spooked financial markets, sent the British pound into a tailspin and drove up interest rates.After passing his Covid relief bill, Mr. Biden managed to push through ambitious legislation to combat climate change. With narrow majorities in the House and especially in the Senate, he had to fend off progressives in his party and win over centrists like Senator Joe Manchin III of West Virginia, who held up that bill until he negotiated compromises with the Senate Democratic leader, Chuck Schumer of New York.The Biden PresidencyHere’s where the president stands after the midterm elections.A Defining Issue: The shape of Russia’s war in Ukraine — and its effects on global markets — in the months and years to come could determine President Biden’s political fate.Beating the Odds: Mr. Biden had the best midterms of any president in 20 years, but he still faces the sobering reality of a Republican-controlled House for the next two years.2024 Questions: Mr. Biden feels buoyant after the better-than-expected midterms, but as he turns 80, he confronts a decision on whether to run again that has some Democrats uncomfortable.Legislative Agenda: The Times analyzed every detail of Mr. Biden’s major legislative victories and his foiled ambitions. Here’s what we found.Mr. Sunak, who has a more than 70-seat majority in Parliament, may not face as much legislative needle-threading in passing his package of tax increases and spending cuts. But he does have to contend with an increasingly unruly Tory Party, which is making it difficult for him to settle a trade dispute with the European Union over Northern Ireland, overhaul Britain’s cumbersome planning rules for home building, or even construct onshore windmills.“He’s being pushed around by various factions in the Tory Party,” said Kim Darroch, a former British ambassador to the United States. “Biden, by contrast, is quite resolute about his moderate, centrist principles.”While Mr. Sunak’s allies make no explicit comparisons between him and Mr. Biden, several have claimed his quiet, unflashy competence is restoring stability after the political roller-coaster of the last three months. On returning to the cabinet as a senior minister, Michael Gove declared “boring is back,” and joked that it was the government’s “utter determination to try to be as dull as possible.”Asked in an interview whether the motif of Mr. Sunak’s leadership was that “boring is the new sexy,” Mark Harper, the transport secretary, smiled and replied: “What he’s about is a government that’s grown up, that grips the issues that people are concerned about and gets on with governing.”Mr. Sunak and his wife, Akshata Murty, returning to 10 Downing Street last month after visiting a food and drinks market promoting British small businesses.Pool photo by Toby MelvilleUnlike Mr. Biden, 80, whose aides still periodically find themselves having to clean up unguarded statements, Mr. Sunak, 42, rarely commits a gaffe. His cautious persona and stilted speaking style have drawn comparisons to John Major, who in 1990 succeeded a more forceful prime minister, Margaret Thatcher.Mr. Major’s electoral record was mixed: He surprised many by winning a modest majority of 21 in the general election in 1992. But that victory was followed swiftly by a financial crisis that sapped his reputation and paved the way for a landslide victory five years later by the Labour Party leader, Tony Blair.This time, the crisis struck before Mr. Sunak took office. But it leaves him with no more than two years to rescue his party before the next election, and he faces the headwinds of soaring inflation, rising interest rates, labor unrest and a recession. Depending on when Mr. Sunak chooses to call that vote, there is a chance that American voters could be electing a president around the same time.Will Mr. Biden be in that race? The chances of his running again rose after the midterms, not to mention the president’s proposal to rearrange the Democratic Party’s primary calendar, so that South Carolina, which resurrected his presidential fortunes in 2020, will now vote first, ahead of the Iowa caucus.There is no evidence that Mr. Biden and Mr. Sunak talked politics in their first face-to-face meeting as leaders at a summit in Indonesia last month. Indeed, given their disparity in age, background and politics, there is little indication they will develop the kind of rapport enjoyed by, say, Mr. Blair and President Bill Clinton. When the Tories elected Mr. Sunak as leader, Mr. Biden hailed it as a “groundbreaking milestone,” though he added, “As my brother would say, ‘Go figure.’”At the moment, the oddsmakers are betting against Mr. Sunak. There is even speculation that if the Conservatives get thrashed in local elections next May, his enemies might move against him and try to reinstall Mr. Johnson. But Mr. Sunak’s allies hope for a Biden-like surprise, which could give him a solid base for the next general election (it must take place by January 2025).Given Labour’s formidable lead in opinion polls — and a Labour leader, Keir Starmer, who rivals Mr. Sunak in competence over charisma — few analysts see a path for Mr. Sunak to a convincing victory. But some think the outcome could be much closer than some of Labour’s supporters now expect. For one thing, Mr. Sunak’s poll ratings exceed those of his battered party, which is the reverse of Mr. Biden and the Democrats before the midterm elections.“There is a big difference between what voters think of the Conservative Party and what voters think of Sunak,” said Peter Kellner, a polling expert. “The big question now is whether the Tory Party drags Sunak’s ratings down, or Sunak drags the Tory Party’s ratings up.”Those are the same questions handicappers were asking about Mr. Biden in the anxious days leading up to the midterms. If both he and Mr. Sunak are in still office in 2025, it will be proof that boring is not only back, but political gold. More