Space, content, curatorial stewardship, patronage, and the embrace of locals and tourists all help determine a museum’s identity and success.

New York is one of the few great museum cities in the world. But its grandest institutions — the Metropolitan Museum of Art, the Museum of Modern Art, the American Museum of Natural History — can be victims of their own prestige: closed to new patrons and artists, and overcrowded with tourists, even with admission charges of $20 a person.

For Los Angeles’s most prominent museums — the Los Angeles County Museum of Art, the J. Paul Getty Museum, the Museum of Contemporary Art — the best is yet to come. Philanthropists and museum leaders have ambitious agendas. However, even with significantly lower admission charges, overcrowding may never be a problem.

“New York is first, L.A. second,” a New York-bred art collector based in Miami, who spends time in both Los Angeles and New York, Mira Rubell, said. “I think that makes it tougher for New York. It’s like being the no. 1 tennis player: You always have to outdo yourself. Los Angeles is less self-conscious. It’s striving. It’s easier to be in second place.”

In New York, financiers and businessmen opened the Metropolitan Museum of Art in 1872 with a collection of more than 150 mostly European paintings; today it has more than 2 million objects. By contrast, Los Angeles’s Museum of History, Science, and Art opened in 1913 without any art in its collections, as part of a cultural center and park. In 1965, Lacma became a separate entity with its own collection, which today includes more than 100,000 objects.

“What New York has managed to do over the past 100-plus years is to not only develop incomparable collections, but also incomparable civic support. It’s that combination that makes it so unique,” the director of the Museum of Modern Art, Glenn Lowry, said. “Los Angeles has the beginnings of a great cultural infrastructure.”

“We have the collections. They have to rely on new shows. We have a long-established audience, and they’re growing and cultivating an audience,” a trustee of MoMA, Donald Marron, said.

The differences have meant great opportunities of for philanthropists in Los Angeles. There, Eli Broad, who built the technology company SunAmerica Inc. from scratch, has shaped the landscape for contemporary art museums. In 1979, he founded the Museum of Contemporary Art, defining its mission, cultivating a board, and hiring a director. In 1984, he founded the Broad Art Foundation, which lends works in his collection. More recently, he has given money to build the Broad Contemporary Art Museum at the Los Angeles County Museum of Art.

As he told an audience at Art Basel Miami Beach in December 2005, “When you’re there at the beginning, you’re a pioneer involved in creating an agenda. … At established institutions that are well run and have a great history, such as MoMA, you just want to be a good trustee and be helpful to the institution to fulfill its mission.” (Mr. Broad joined the MoMA and Smithsonian Institute boards in 2004).

Mr. Broad’s involvement at Lacma and MoMA led to a co-acquisition by the institutions of “Hell Gate” by Chris Burden. The unusual arrangement lets both institutions display the work and share in the costs of storing it.

New York’s art world is closely watching Lacma, whose 20-acre campus is undergoing a Renzo Piano–designed transformation that is expected to be complete by next year.

Its director, Michael Govan, is well known and admired in New York, having moved west for the Lacma post less than a year ago, after heading the Dia Foundation for 11 years and working at the Guggenheim.

“Govan being at Lacma means a lot to the city. He’s raising the bar here,” Los Angeles art dealer Shaun Caley Regan of Regan Projects said.

Accordingly, Lacma’s board of trustees is growing (recent additions include author Michael Crichton and Yahoo chief Terry Semel). And so are its collections. Last year the value of Lacma’s 320 acquisitions and gifts, $40 million, was nearly twice what the museum had averaged in the past 20 years.

In New York, space is at a premium, making expanding a headache for numerous museums, most recently the Whitney. Los Angeles institutions have an easier time with real estate. So do artists. “L.A.’s largesse in real estate means it’s a place that artists can live. In New York, every artist’s community is being destroyed,” sculptor Sean Mellyn, who lives in Dumbo, said. “New York will stay a place to buy art and to view art, but not a place to make art.”

New York attracts a larger number of cultural tourists who help keep the city the place to view art. Los Angeles has been less successful. “Our biggest challenge is the weather. It’s so temperate here, the last thing people coming here from Detroit or Boston want to do is be in a windowless building,” the head of the cultural tourism program at the Los Angeles Convention & Visitors Bureau, Michael McDowell, said.

But Mr. Broad thinks otherwise. “Los Angeles can be the contemporary art capital of the world,” he said at the 2005 Art Basel Miami Beach event. “I’ve got great aspirations, as do others.”