Updated

Hillary Clinton's Senate seat has emerged as the prize to be won in a battle of influence between East Coast political dynasties.

On one side, the Kennedys. On the other, the Cuomos.

A field of nearly a dozen possible candidates to replace New York's junior senator, who is leaving the Senate to potentially become Barack Obama's secretary of state, has been overshadowed by those family names.

And a standoff between Caroline Kennedy and state Attorney General Andrew Cuomo could be the next political drama.

The contest is complicated by family ties between the Kennedy and Cuomo clans that date back two decades. And then there are the Clintons, who some observers expect will leave their fingerprints on the replacement process.

The decision of who replaces Clinton is legally up to Gov. David Paterson. Once Clinton resigns, he must appoint someone to serve until 2010, when the state will hold a special election to fill out the remaining two years of the term.

But the process that unfolds over the next several weeks could demonstrate which clan -- the Kennedys or Cuomos -- holds the clout, both in New York and in national Democratic politics.

"They both are forces to be reckoned with, and their families are forces to be reckoned with in their own way," Maria Cardona, a Democratic strategist and former Hillary Clinton adviser, said of the two families. She added: "You can be sure that Governor Paterson will know where both Senator Clinton as well as President-elect Obama stand on this."

In public, Obama says he's not getting involved. He told NBC's "Meet the Press" Sunday that Caroline Kennedy, who endorsed Obama early on, along with her uncle, Sen. Ted Kennedy, has "become one of my dearest friends." But, he said, "The last thing I want to do is get involved in New York politics."

Based on resumes alone, Kennedy, who also helped steer Obama's vice presidential vetting process, would seem to have more going for her in Obama's book than Cuomo. But Cuomo, who served as a Cabinet secretary under Bill Clinton, would seem closer to the Clintons.

Kennedy brings her own set of attributes to the table. First, she is a woman, and Cardona noted that's women's groups want Paterson to pick a woman to replace Clinton. The debate is similar to one in Illinois, where Rep. Bobby Rush has called for Gov. Rod Blagojevich to replace Obama, who was the only black member of the Senate before he resigned, with another black candidate.

But Kennedy, the daughter of former President John F. Kennedy and the niece of former New York Sen. Robert F. Kennedy, is also an accomplished author and education advocate. As her uncle Ted Kennedy battles a malignant brain tumor, Caroline Kennedy could be seen as carrying on her family's legacy in the Senate. And as Robert F. Kennedy Jr. told The Associated Press, the Kennedys will come out in droves to support her when the 2010 special election comes around.

"She's somebody who thinks about things, and I think in this environment, in the kind of presidency Barack Obama is likely to have, she would be a very good antidote to the excessive partisanship of Washington," Democratic strategist Doug Schoen said.

But there's no counting out Cuomo just because he's going up against the mighty Kennedys.

Foremost, he is a New York figure, the son of former Gov. Mario Cuomo.

Cuomo, who was elected state attorney general in 2006, will be the favorite if the decision is truly up to Albany, New York State Assembly Majority Leader Ron Canestrari told FOXNews.com.

"In terms of being in the political trenches, Andrew has been here in New York state with his father and on his own," he said. "We've read about [Caroline Kennedy], but we've worked with Andrew Cuomo, and that makes a difference."

Plus, Canestrari said, Cuomo has run statewide and has been elected before. Kennedy hasn't.

Patrick J. Egan, assistant professor of politics at New York University, said Democrats -- who are so close to a filibuster-proof majority in the Senate they can almost touch it -- will probably make a "cold, hard political calculation" when it comes to replacing Clinton.

And given Cuomo's sheer ambition and past electoral success, he said the sense among the party would be, "He's someone who can reliably deliver the seat back to the Democrats in 2010."

Kennedy has name recognition, but the Kennedy family can't always win an election on star power alone. Egan noted that Kathleen Kennedy Townsend, daughter of Robert F. Kennedy, lost the race for Maryland governor to Republican Robert Ehrlich in 2002.

Egan said national forces will surely be at play in the process of replacing Clinton. "It's certainly not Paterson's decision alone."

Family politics might enter the arena as well. Andrew Cuomo was once married to Kerry Kennedy, a daughter of Robert Kennedy, until their divorce in 2003. They have three children.

Until recently, it seemed like Cuomo was the front-runner. A Marist poll showed 43 percent of New York voters want to see Cuomo replace Clinton.

But then reports leaked over the weekend that Kennedy had spoken with Paterson about the job. The dynamic suddenly changed, and other candidates like Reps. Carolyn Maloney and Kirsten Gillibrand seemed somewhat diminished.

In New York, Paterson was asked Monday whether he would consider someone, like Kennedy, who never had been elected to office.

"Absolutely," said Paterson. "Elected office is not the only place that people have distinguished themselves and can serve the public."

New York City Mayor Michael Bloomberg also praised Kennedy as "very experienced."

Bill Cunningham, former spokesman for Bloomberg and former staffer for Mario Cuomo, told FOXNews.com that Kennedy has an advantage in that her family can lobby for the job in a way the Cuomos can't.

But he said the result of this political battle might rest in whether Caroline Kennedy -- until this past year a very private figure with a famous last name -- really wants to subject herself and her family to the scrutiny of national public office.

"The real question is, at this time, do you want to step into the full glare?" he said.

FOXNews.com's Judson Berger and The Associated Press contributed to this report.