"I have enormous respect for Warren for what he's accomplished. He's an investment genius," said Cooperman.
Cooperman, a former general partner at Goldman Sachs, said Buffett has always been "more focused on making (money) than giving it away" and wanted the wealth to grow through compounded interest before turning to the Gates Foundation later in life as a vehicle for his giving.
One area where Buffett wasn't as focused was on David Sokol, once considered his heir-apparent, and Berkshire's purchase of Lubrizol, Cooperman said.
A new proxy filing Tuesday shows Sokol was informed by Lubrizol's Citigroup bankers as early as Dec. 17, before he bought a second round of shares in the chemical company, that the Lubrizol board was going to discuss Berkshire Hathaway's interest in buying the company. Sokol has since left Berkshire.
"The mistake that was made was (Sokol) should've sold his stock the moment he went to Buffett. Having failed to do that, he should've said he was happy to donate the money to charity," Cooperman said.
Another area where he disagreed with Steinhardt was on hedge fund size versus performance. Where Steinhardt saw hedge funds sacrificing performance to accumulating assets under management and collecting fees, Cooperman sees size as "an anchor to performance."
"I know of no hedge fund that used a gun or a mask to attract their clients. The clients are not fools. If the clients weren't getting what they're looking for they wouldn't invest in the hedge funds."
Cooperman said it is "still appropriate to be optimistic" about the stock market as the economy begins to recover, but "have a tempering of your optimism."