Fifteen years after the death of its founder, the Alvin Ailey American Dance Theater celebrates its 40th anniversary at City Center, as well as the completion of its snazzy new building, the Joan Weill Center for Dance. Downtown at the much smaller Joyce Theater, Ballet Hispanico honored 35 years of existence under its founder-director, Tina Ramirez. Ramirez recently told an interviewer that she hoped her company’s season would attract a new young crowd. At the Ailey opening gala, artistic director Judith Jamison said with sly pride, “We don’t mind being a popular company.” In other words, both the large (32 dancers), world-famous AAADT and the smaller (13 dancers), also-known-abroad Hispanico promote choreography that mingles passion and artistry with display, presenting dances that may encompass subtlety but never confuse people. Ailey, his taped voice heard intermittently through the new Love Stories, said he wanted his work to “hold a mirror to our society so people can see how beautiful they are.”

“Beautiful” is the operative word—rather than, say, complex, intelligent, or disturbed. Strife is cloaked in beauty. And beauty the dancers always deliver. An opening-night house that included Jesse Jackson and honorary gala chairman Derek Jeter received it with cheers.

Love Stories is a showy hodgepodge by three choreographers—Jamison, Rennie Harris, and Robert Battle—unified mainly by Darrin Ross’s score, which incorporates and transforms Stevie Wonder’s music. Despite Ailey’s recurring voice, it only intermittently alludes to the company’s history. You can certainly see Ailey’s mission, and a hint of the supremely beautiful dancer he once was, in the solo Jamison has created for the equally gorgeous Clifton Brown, who wields his long limbs with velvety strength. And Jamison’s portion of the work shows the dancers socializing and practicing steps (Hope Boykin, yes!).

Harris’s section is strong. He’s retained the pulse and bite of the hip-hop steps he grew up with—and a smattering of their acrobatics—while incorporating elements of the Ailey performers’ modern-dance training in his smart, neat choreography (Dwana Adiaha Smallwood can shake everything she’s got and still look precise). After the golden Matthew Rushing travels along a path of light, Battle churns up chorus lines and breakouts into celebratory wildness.

Love Stories doesn’t give a deep, consistent vision of what the Ailey troupe is all about. It says, “Don’t you love these dancers?” “Yes!” screams the crowd.

Donald Byrd’s Burlesque, the company premiere of a 2002 work, shows off the Ailey dancers’ skill at robust portrayals. Draped red curtains and footlights (by Jack Mehler) turn the stage into a burlesque house, where, to music by Louis Armstrong, entertainers in tackily gaudy costumes by Emilio Sosa perform, squabble, drink, and slump in chairs at the back. Onstage and backstage behaviors merge so bizarrely that this might be a burlesque performer’s hell rather than an in-depth evocation of an era in showbiz. What’s not to enjoy, though, about Glenn Allen Sims’s audience-cozening and perpetual smile, Brown’s sad-sack persona, Abdur-Rahim Jackson’s goofy innocence, and in-fighting and valiant bouts of dancing by Linda-Denise Fisher-Harrell, Briana Reed, Olivia Bowman, and the always marvelous Asha Thomas?

Ballet Hispanico’s new drawing card is Eternamente y un Día, by Peter Pucci. A veteran of Pilobolus, Pucci is savvy about making designs with bodies, and his work on plays, commercials, and industrials (in addition to maintaining his own company) has put him further in touch with drama and pleasing an audience. The new piece’s only binding theme is Mexican culture, and its only unifying elements are the costumes (black pants and variously colored tops by Toni-Leslie James) and the Kronos Quartet’s fascinating performance, on the recording Nuevo, of music by Latin composers. Pucci segues, sometimes with startling alacrity, from celebratory dances to ritual ones, from love and death to partying. Contrast abounds—exciting when dancers silhouetted against a red background advance into light and three-dimensionality as their feet begin to heel-and-toe and their bodies to twist; entertaining when the talented performers go from imitating lizards, chickens, and monkeys to whipping through a pleasingly choreographed carnival of acrobatics to miming with stagy glee the breaking of a piñata. But only a change of Howell Binkley’s lighting prepares us for a slow, sensuous solo by Irene Hogarth-Cimino, whose rite of passage ends with the other women giving her invisible gifts and the men lifting her high—the same men who then execute a strong, stamping dance of machismo.

Duets are de rigueur in suites like this, and Pucci creates some fetching ways of merging two bodies. There’s something dramatically murky about this section, though. Does Sara Kappraff die because those five men tossed her along? Is that why she’s lying in a square of red light with Eric Rivera mourning over her? When barely visible black-clad figures lift her, she comes to life. All a mistake? Resurrected by love? Whatever. The lovers get their pas de deux, and everyone goes to the fiesta, women letting down their hair right on the beat.

Ballet Hispanico has also remounted and revised Ramón Oller’s vibrant if uneven take on gypsy culture, Bury Me Standing, in which Pedro Ruiz gives an especially outstanding performance. Superb, too, is Natalia Alonso in William Whitener’s choreographically rich 1983 solo Llamada.