But, in a change of tone, the former vice president acknowledged that the Bush White House had struggled with how to bring terror suspects to justice.
Public skirmishes between the Obama White House and Cheney, the result of the ex-vice president's unusual public criticism on a successor administration, have become standard. And the back-and-forth in sequential appearances on the Sunday TV talk shows did not disappoint.
Biden struck first, declaring that Cheney's attacks on Obama's commitment to fighting terrorism ignored the facts.
"We've eliminated 12 of their top 20 people. We have taken out 100 of their associates," said Biden. "They are in fact not able to do anything remotely like they were in the past. They are on the run. I don't know where Dick Cheney has been."
Cheney did not answer directly, instead insisting that Biden was "dead wrong" to assert that a fresh Sept. 11-style strike was unlikely, calling a nuclear or biological attack by al-Qaida "the biggest strategic threat the United States faces today."
Even so, Cheney appeared to dial back the rhetoric, acknowledging the Bush administration, too, was divided on whether terror suspects should be tried in civilian courts or taken before military tribunals. "I can remember," he said, "a meeting in the Roosevelt Room in the West Wing of the White House where we had a major shootout" - one that he said he lost - about civilian versus military trials, for terrorist captives. "We never clearly or totally resolved those issues," he said on ABC's "This Week."
Biden got in the first licks on NBC's "Meet the Press." On Cheney's assault on the Obama administration, Biden said "his assertions are not accurate." Cheney demurred on that allegation, choosing instead to take on again Obama's decision to close the U.S. military prison at Guantánamo Bay, Cuba.
In doing so, he again admitted that he'd been at odds with most Bush officials on the decision to release prisoners from the lockup to their home country when cases against them were determined to be legally untenable.
"I didn't think that releasing anybody was the right thing to do, unless you had evidence that, you know, there was a mistake of some kind," Cheney said.
Cheney praised Obama for increasing U.S. forces in Afghanistan. But he derided Biden for giving the Obama administration credit for winding down the Iraq war without acknowledging President George W. Bush's work.
But Biden said: "We built on the positive things that the Bush administration had initiated. And we have jettisoned those things that were negative."