When the two discussed Israel's security, Biden said he understood how Sharon earned the nickname "The Bulldozer," explaining how Sharon would pull out maps and repeatedly make the same points to drive them home.
"He was indomitable," Biden said. "But like all historic leaders, all real leaders, he had a north star that guided him. A north star from which he never, in my observation, never deviated. His north star was the survival of the state of Israel and the Jewish people wherever they resided," Biden said.
Sharon died on Saturday, eight years after a devastating stroke left him in a coma from which he never recovered. He was 85.
One of Israel's greatest and most divisive figures, Sharon rose through the ranks of the military, moving into politics and overcoming scandal and controversy to become prime minister at the time of his stroke.
He spent most of his life battling Arab enemies and promoting Jewish settlement on war-won lands. But in a surprising about-face, he led a historic withdrawal from the Gaza Strip in 2005, uprooting all soldiers and settlers from the territory after a 38-year presence in a move he said was necessary to ensure Israel's security.
His backers called him a war hero. His detractors, first and foremost the Palestinians, considered him a war criminal and held him responsible for years of bloodshed.
The speakers at Monday's ceremony outside parliament largely glossed over the controversy, and instead focused on his leadership and personality.
"Arik was a man of the land," President Shimon Peres, a longtime friend and sometimes rival, said in his eulogy. "He defended this land like a lion and he taught its children to swing a scythe. He was a military legend in his lifetime and then turned his gaze to the day Israel would dwell in safety, when our children would return to our borders and peace would grace the Promised Land."
Prime Minister Benjamin Netanyahu, who resigned from Sharon's Cabinet to protest the Gaza withdrawal, said that he and Sharon didn't always agree with each other. Nonetheless, he called Sharon "one of the big warriors" for the nation of Israel.
"Arik was a man of actions, pragmatic, and his pragmatism was rooted in deep emotion, deep emotion for the country and deep emotion for the Jewish people," Netanyahu said.
Nearly 10 years on, the withdrawal from Gaza remains hotly debated in Israeli society. Supporters say Israel is better off not being bogged down in the crowded territory, which is now home to 1.7 million Palestinians.
Critics say the pullout has only brought more violence. Two years after the withdrawal, Hamas militants seized control of Gaza and stepped up rocket fire on Israel.
In a reminder of the precarious security situation, Palestinian militants on Monday fired two rockets from the Gaza Strip. Sharon's ranch in southern Israel, where his body was being laid to rest, is within range of such projectiles, though but Monday's missiles did not hit Israel. No injuries or damage were reported.
Biden praised Sharon's determination in carrying out the Gaza pullout, which bitterly divided the nation.
"The political courage it took, whether you agreed with him or not, when he told 10,000 Israelis to leave their homes in Gaza, in order from his perspective to strengthen Israel ... I can't think of a more difficult and controversial decision he made. But he believed it and he did it. The security of his people was always Arik's unwavering mission."