Odd to have Nixon administration and campaign veterans such as Lamar Alexander and Karl Rove calling Obama Nixonian. As a matter of fact, the charge manages to disserve both Presidents.
As MK notes in a comment here, President Nixon's media strategy was more discerning than most remember. That being said, as Joe Conason reminds us, RN's aides John Dean and Chuck Colson accumulated the names of his administration's critics for what became known as the enemies list. Dirty tricks were never justified. But Conason doesn't point out that President Nixon had inherited a war that was much more complex and costly than Afghanistan while trying to govern in a far more hostile global, political, and media environment. While Nixon critics like to say that his abuses of power were sui generis, so too was the poisonous temperament of his times. Obama's party controls Congress. Nixon's did not. Obama has Fox overtly against him. Nixon had most reporters and editors voting against him and some, at least, subtly prosecuting political agendas. Obama has tea parties. Nixon had firebombings, riots, efforts to shut down Washington, and Kent State. In his book In the Arena, Nixon took responsibility for inculcating a corrosive us-vs.-them mentality in the White House. Few if any of his often vicious ideological critics ever did the same.
By the same token, Conason is right that Obama's public posturing against Fox News isn't comparable to the Nixon administration's behind-the-scenes efforts to punish media adversaries for their perceived bias. In at least one sense, though, nothing has changed. Some who were put on the enemies list are still bragging about it. In the same spirit, most Fox personalities are cheerfully brazen about promoting Obama's demise. They make an incredibly tempting target, and now that Obama and his aides have aimed and fired, Fox couldn't be happier as it totes up its bolstered ratings.
Anderson Cooper probably compared Obama to Nixon to avoid the charge that CNN wasn't being fair and balanced. I don't think he believes it for a second. The media don't have it anywhere near as bad as they did under Nixon, and Obama doesn't have it anywhere near as bad as Nixon did.