Mueller and Joshua Henry in “Carousel” at the Imperial Theatre on Broadway. (Julieta Cervantes)

As it turns out, the Broadway musical addressing the issue of bullying most provocatively this season isn’t “Mean Girls.” 

It’s “My Fair Lady.”

And the lavish revival of Lerner and Loewe’s 1956 masterwork gets strong competition for this distinction from yet another gorgeously sung remounting on Broadway of a musical from the past: Rodgers and Hammerstein’s “Carousel.” For just as cockney flower girl Eliza Doolittle is browbeaten by a brute of otherwise tweedy civility — Prof. Henry Higgins, in “My Fair Lady” — so is New England factory worker Julie Jordan manhandled by a brute of cruder instincts — “Carousel’s” carnival barker Billy Bigelow.

It is, in this year of raised consciousness about the ways men seek to physically and psychologically control women, of particular note that of all the musicals that could wind up back in the theater world’s most celebrated district, these two should be selected. Based on European plays written by major male dramatists after the turn of the 20th century, both hinge on the transformation of a central male character whose foremost transgressive act concerns abusing a young woman.

But an audience in 2018 finds itself far more intrigued by those women, and in the productions that have officially opened within a week of each other — “Carousel” on April 12 at the Imperial Theatre and “My Fair Lady” on Thursday night at the Vivian Beaumont Theater — these portrayals are some of the evenings’ finest aspects. Jessie Mueller’s Julie of touching forbearance and Lauren Ambrose’s Eliza of steely self-possession seem far more than the love objects from whom the male characters are supposed to learn. The talented actress-singers, both showing off galvanizing vocal instruments, make so abundantly clear the qualities of resilience and generosity in Julie and Eliza that we’re compelled to the certainty that the unworthy men who seek to keep them caged are baser characters.

In this regard, and in other handsome ways, “My Fair Lady” proves to be the more fully satisfying of the two evenings. Director Bartlett Sher locates in Ambrose and Harry Hadden-Paton — the smashingly immature Henry of this exhilarating Lincoln Center Theater revival — a matchup that reveals the ecstatic extent of Eliza’s development. Not simply as Covent Garden flower girl to lady of Ascot: That does, of course, occur, in the remarkable metamorphosis Ambrose affects and the soignée gowns Catherine Zuber designs for her. Lost child-to-independent-woman is the more intriguing change, one that comes to the fore more vividly in this revival than perhaps in any previous version.

All of the famous numbers are winningly mustered on the massive Beaumont stage by Sher and choreographer Christopher Gattelli, particularly in “Ascot Gavotte,” “The Rain in Spain,” “I’ve Grown Accustomed to Her Face” and a bewitching “I Could Have Danced All Night.” Yet the signature song on this occasion is the one Eliza delivers as the summation of the case against Henry’s self-infatuated oppressiveness: “There’ll be spring every year without you/ England still will be here without you,” Ambrose sings in “Without You,” an energetic indictment that grandly sets up the apt refinement Sher applies to the musical’s final moment — one more faithful to George Bernard Shaw’s original play than the conclusion more sympathetic to Henry fashioned by Alan Jay Lerner. The song stamps Eliza’s journey as complete.

The fablelike “Carousel” presents an even more urgent moral conundrum: Its antihero, Billy, played with muscular vocal command by Joshua Henry in director Jack O’Brien’s half-great revival in the Imperial Theatre, uses his fists to punish his wife. The issue of how hard or often is debated here, and even more frequently in “Liliom,” the 1909 play by Ferenc Molnar on which Rodgers and Hammerstein based the musical. That abuse arises as a plot point is not so much a problem — the issue is still pertinent — as is the antique way it’s characterized in the musical: not as a serious crime, but as a character flaw.

Billy’s search for redemption becomes the preoccupation of the musical’s second act, which occurs in a creaky approximation of the afterlife. The saving grace is what just might be the dreamiest score in the R&H canon. If the swoony tones early in the evening of “If I Loved You” sung by Mueller and Henry, don’t win you over, Renée Fleming is on hand with a beguiling Act 2 rendition of “You’ll Never Walk Alone.” (Choreographer Justin Peck, meanwhile, contributes heart-stopping steps for the corps of male dancers in “Blow High, Blow Low.”)

But thanks to Mueller, Julie is the quiet and fully activated force to be reckoned in this revival. She’s provided with exceptional backup by Lindsay Mendez’s Carrie Pipperidge, an exuberant counterpoint to the empathetic introvert Mueller portrays. Although “Carousel” barely offers occasion to show us an untroubled moment for Julie, Mueller’s emotionally centered performance firmly establishes that Julie owns her choices and that her passion for Billy remains alive even after he is gone. That may not wash away our discomfort with some of the more disturbing aspects of a 1945 musical, particularly because Julie’s quest for healing might make a far more compelling basis for a musical than the plot that intrigued a songwriting team more than 70 years ago.

My Fair Lady, book and lyrics by Alan Jay Lerner, music by Frederick Loewe. Directed by Bartlett Sher. Choreography, Christopher Gattelli; music direction, Ted Sperling; sets; Michael Yeargan; costumes, Catherine Zuber; lighting, Donald Holder; sound, Marc Salzberg. With Norbert Leo Butz, Allan Corduner, Linda Mugleston. About 2 hours 50 minutes. $97-$399. At the Vivian Beaumont Theater, 150 W. 65th St., New York.

Carousel, music by Richard Rodgers, book and lyrics by Oscar Hammerstein II. Directed by Jack O’Brien. Choreography, Justin Peck; sets, Santo Loquasto; costumes, Ann Roth; lighting, Brian MacDevitt; sound, Scott Lehrer; orchestrations, Jonathan Tunick. With Margaret Colin, Amar Ramasar, John Douglas Thompson. About 2 hours 45 minutes. $59-$169. At the Imperial Theatre, 249 W. 45th St., New York. For both shows, 212-239-6200 or telecharge.com.