Bob Woodward’s new book, “The Price of Politics,” makes him the latest in a string of Washington cognoscenti to compare Barack Obama’s personality unfavorably with Bill Clinton’s and to suggest that Obama’s presidency would be more successful if he were less introspective and aloof, more outgoing and more of a schmoozer. Although Woodward and pundits such as The Post’s Richard Cohen [“The solitary executive,” op-ed, Sept. 5] acknowledge the head winds that Obama has faced — an implacable Republican opposition, a surfeit of sulfurous anti-Obama rhetoric, racism sometimes only thinly disguised — they still lament Obama’s failure to return phone calls or to buddy up to business leaders or to have beers with members of Congress, traits that never would have been attached to Clinton.

The stylistic differences between Obama and Clinton are stark. But the comparison ignores larger realities about both presidencies. The first is how well Clinton’s open and enveloping approach worked to improve his presidential performance. And the answer is . . . not much, if at all.

From the beginning of his presidency, Clinton was under an all-out assault from Republican leaders and their acolytes and mouthpieces in the conservative media. He was also remarkably accessible to a wide range of allies and adversaries — constantly in contact with a mind-boggling collection of people to get ideas and gauge performance — just the kind of thing that Woodward and Cohen suggest should have a payoff. But Clinton’s engagement did not stop or even temper the attempts to delegitimize him. “Slick Willie” was perhaps the nicest epithet applied to him; the Wall Street Journal editorial page suggested several times that the president might have been an accessory to murder while governor of Arkansas. When Vince Foster wrote in his suicide note about how politics in Washington was a blood sport, he referred to the personal attacks not only on him but also on the president and the first lady.

Of course, many of those attacks flowed from self-inflicted wounds, but in most cases the Clinton missteps were amplified into huge errors or crimes by the anti-Clinton wind machine, which was not deterred by the president’s warm style.

At the same time, Clinton tried tirelessly to reach out to Democrats in Congress as well as Republicans. But all of the phone calls, flattery and schmoozing did not stop Republicans in both houses from voting in unison against the Clinton economic plan, and for almost eight months of humiliation and deadlock he did not have enough votes from his own Democrats. When the plan finally passed, by a single vote in each house, it came across as more of a setback than a triumph. And the schmoozing on the health-care plan did not stop Republican Senate leader Bob Dole from blocking action on any compromise reform, nor did it bring together enough Democrats to avoid the devastating defeat of the signature Clinton effort that led to the Republican sweep in the 1994 midterms.

To be sure, after Clinton’s adroit handling of the ham-handed GOP effort to shut down the government in 1995, Republicans under House Speaker Newt Gingrich dealt with the president differently. They cooperated on welfare reform and on a budget agreement in 1996. But that cooperation had little to do with Clinton’s outgoing style; it was a hard-nosed calculation by Gingrich that cooperating would ensure that Republicans could win a second consecutive majority in the House, even if it damaged Dole’s presidential prospects. And barely a year after the 1996 election, Republicans were hammering the president again, culminating in his impeachment by the House.

On balance, Clinton was a good and strong president. But — and here is the second reality — it was Obama, in an even more intransigent and tribal era, who got a major health-reform package through a bitterly divided Congress. As Michael Grunwald details in “The New, New Deal,” Obama also managed to enact a major set of substantive policies — including financing the introduction of information technology into the health-care system, expanding broadband and revamping the electrical grid — that had eluded his predecessors. The accomplishments of the 111th Congress rivaled those of the Great Society Congress of Lyndon Johnson’s era. And they were achieved without the midnight phone calls or warm interactions with allies and adversaries that characterized Clinton. To a large extent, they were achieved because Obama gave his leaders in Congress a lot of slack to find majorities (or supermajorities) and intervened only when a push was needed.

If Obama had been more like Clinton, he might have ameliorated some of the tough rhetoric used against him by many business leaders and nabobs of the financial industry whose businesses, and fortunes, he saved. He might have put more onus on Republican leaders who undercut him at every turn, even before he was inaugurated, to explain their intransigence. Such an approach certainly would have cheered a lot of people who loved those communications with Clinton but who have had none of it with Obama (me among them). But it would not necessarily have made Obama’s presidency less contentious or his accomplishments more robust.