Mayor Bloomberg here and Mayor Villaraigosa in Los Angeles each have high public approval ratings and are both being buzzed about for higher office. But their city governments are entirely different beasts.

“It’s so different from New York it’s like a different planet,” a Democratic strategist in Los Angeles, Darry Sragow, said. “For one thing we have historically had a very weak mayor, who has far less brute power than the mayor does in New York.”

The City of Los Angeles, which has a population of about 3.96 million people, is part of the larger Los Angeles County, which has a total population of about 10 million and governing authority over a wide array of services. Then there is the Los Angeles Unified School System, whose seven-member elected school board controls the region’s education system, and the area’s transit authority, which controls the rails trains and city buses.

The more de-centralized government — which in the city includes a 15-member council and in the county is comprised of a powerful five-member board of supervisors — means more checks and balances, but a more complicated and slower process for getting things accomplished.

It also leaves far fewer purse strings for Mr. Villaraigosa in his city than it does for Mr. Bloomberg here. The budget for Los Angeles County — which includes 88 cities, most with their own mayor and town council — is about $20 billion. That is in addition to a budget of $6.67 billion for the City of Los Angeles and the budgets of the other cities within the county, like Beverly Hills, Malibu, and Santa Monica. By comparison, the budget for New York City last year was more than $55 billion.

The police commissioner of the City of Los Angeles, William Bratton, who served as New York City’s police commissioner for part of Mayor Giuliani’s tenure, said he has both more bureaucratic hoops to jump through in Los Angeles and far fewer resources.

The city, which has a reputation for being one of the most underpoliced in the nation, has 9,407 uniformed officers compared to New York’s 37,038. That does not include the 12,700 uniformed police in Los Angeles County.

Mr. Bratton, who introduced the now-famed crime-tracking system CompStat in both cities, said his wife, the TV commentator and attorney Rikki Klieman, describes seeing a police squad car in Los Angeles as a “sighting.”

“You can literally ride around this city and never see a police car,” Mr. Bratton said during a telephone interview earlier this week. “In New York, you can’t step off a curb without almost getting run over by one.”

He said the resources he had in New York under Mr. Giuliani, when crime decreased by double digits, allowed him to “put a lot of pressure everywhere.” Mr. Bratton resigned in 1996. Mr. Giuliani reportedly wanted Mr. Bratton out because he was upstaging him.

“Here I function more as a fire department,” Mr. Bratton said. “I respond to the latest crises, or outbreak of crime, or anticipated outbreak of crime, but then I have to leave.”

Mr. Bratton said despite the additional oversight he faces, he has the same goals as New York’s Police Commissioner, Raymond Kelly, of reducing crime and preventing terrorism.

Meanwhile, Mr. Villaraigosa has been shaking the political power structure since knocking out incumbent James Hahn last year. In Bloomberg fashion, he was granted partial control of the school system, but has not yet been able to implement it because it’s being challenged in court.

While his predecessor was largely invisible, Mr. Villaraigosa seems determined to exercise more political power and to use his bully pulpit to push for change. That, coupled with his charisma, already has the political establishment speculating on whether he’ll run to replace Governor Schwarzenegger in the future.

Some say that means a leaner government in Los Angeles, but most political analysts and professors said government plays a much smaller role in Los Angeles, largely because it offers fewer services. They also say that residents in Los Angeles, who rely more on their cars and less on public transportation that New Yorkers do, also have less interaction with government.

A professor of management and public policy at UCLA, Daniel Mitchell, traced the de-centralized government to progressive reform movement in California in the early 20th century. Others said residents there have a libertarian streak.

“Attitudes about government and politics in Los Angeles are roughly 180 degrees away from those in New York,” Mr. Sragow said. “Californians by and large think that government can’t shoot straight, and the less government we have the better off we all are.”