André Holland and Danai Gurira in ’Measure for Measure,’ performed by Shakespeare in the Park.  (Joan Marcus)

Bill this midsummer card as an Elizabethan throwdown: the Royal Shakespeare Company versus the New York Shakespeare Festival. Virtually within earshot of each other, Britain’s bastion of Bard-dom and Manhattan’s warm-weather outlet for iambic pentameter are presenting a passel of plays, and in the process begging for some comparing of contemporary national styles for playing Shakespeare.

And here are the shocking early returns: These rounds go to the Yanks. With its one-two punch of “Measure for Measure” and, even more incandescently, “All’s Well That Ends Well,” the Joseph Papp Public Theater’s Shakespeare in the Park is offering a pair of more supple and provocative evenings than the initial two RSC presentations at the Park Avenue Armory of “As You Like It” and “Romeo and Juliet.”

I’ll grant you that it’s a dicey business, generalizing too broadly from a few productions. Still, experiencing this quartet of Shakespearean nights does turn conventional wisdom on its head. Many of us — nourished by a golden generation of stars with names like McKellen and Dench — have been so conditioned to regard British Shakespeare as the superior invention that we’ve tended to think of the American version as lacking some genetic adhesion to the verse and its myriad shadings of meanings.

I’ve seen enough American Shakespeare now, courtesy of Shakespeare Theatre Company and other organizations, to understand that my early prejudices were based on a lack of adequate exposure. It remains apparent that for inspired direction, the ranks of Shakespeare interpreters in this country could be fuller. Actors here, though, have embraced the Bard with ever more impressive energy, subtlety and confidence. And when guided by a serious director, whether it’s Robert Falls for tragedy, Michael Kahn for comedy or Daniel Sullivan for a knotty problem play, the results are as persuasive as anything from the opposite side of the pond.

The surest support for this assertion is provided by Sullivan, who at Central Park’s Delacorte Theater has staged “All’s Well” — one of Shakespeare’s most peculiarly plotted works — as a compellingly complex romance with a moving core. It’s the best of the four nights. By virtue of the production, Sullivan, director of last summer’s altogether commanding “Merchant of Venice” with Al Pacino, ascends categorically to the top tier of American Shakespeare directors. Though he had a bad Broadway run-in several years ago with “Julius Caesar,” starring a wooden Denzel Washington, he demonstrates with his “All’s Well” that any time you assert that a given Shakespeare work is unwatchable, it just means the right production hasn’t come along.

This is the right “All’s Well.” It’s one of Shakespeare’s more perverse takes on love: Helena (a beguiling Annie Parisse) has her heart set on Bertram (the born Shakespearean, Andre Holland), who seems to detest her. For the next 2 3 /4 hours, Helena wages the sort of single-minded pursuit — in bedrooms and across battlefields — that would have exhausted the rabbit-boiling Glenn Close of “Fatal Attraction.”

You are compelled to wonder here: Why is it when men go overboard for love, it’s called passion, and when women do, it’s obsession? Parisse neutralizes the dislike one might harbor for the aggressive Helena by making her a softly self-assured creature. And buoyed by Tonya Pinkins’s gentle Countess of Roussillon and John Cullum’s virile King of France, this Helena receives the sturdiest emotional and monarchial support for her quest. Sullivan, sharply, injects additional justification, with the suggestion that Bertram against his better judgment is just a tad turned on by his ardent admirer.

The completeness of “All’s Well’s” textures is embodied by the surefire antics of Reg Rogers as Bertram’s aide, the puffed-up coward Parolles. And the play’s companion in the Park’s revolving repertory, director David Esbjornson’s “Measure for Measure,” boasts other exemplary performances, most notably from Danai Gurira and Michael Hayden. They are delivering portrayals by turns magnetic and of superb intensity as combatants across the piece’s fascinating moral divide.

What’s missing in the RSC entries — two of the five plays the company has brought to New York this summer as part of the Lincoln Center Festival — is a comparable joy. Indeed, the most exhilarating facet of the visit may be the extraordinary temporary theater that has been constructed in the cavernous armory: a tri-level playhouse with runway stage thrusting us into the action.

One is immersed in lucid demonstrations of technique from such fine young RSC actors as Katy Stephens, as a protean Rosalind in director Michael Boyd’s “As You Like It,” and Sam Troughton and Mariah Gale as the circa 2011 impulsive teens of Rupert Goold’s time-bending “Romeo and Juliet.” Off their lips and tongues, the poetry sounds grand — grander than in Central Park. And the dissection of text carries on in a profound manner: Troughton and Gale’s deft line readings in the balcony scene, for instance, suggest that the connection here is as much a flaring of adolescent intellect as flesh. These two conjoin as besotted AP students.

Yet you’re also left with the impression, especially in the weakest night, Boyd’s disappointingly inert “As You Like It,” of a self-conscious studiousness, an effort virtually to diagram the various thematic strands of the play. (The abstracted set and its gags — enter Richard Katz’s Touchstone, trapped in a bubble of brambles — come across aridly.) The deepening love between Rosalind and Jonjo O’Neill’s Orlando never becomes resonant.

The RSC visited the Kennedy Center annually for several years in the 2000s, and some of those visiting productions, such as 2007’s ferocious “Coriolanus,” evinced more of the company’s voracious attack of yore. Maybe a convergence is needed — more exchanges that are variations of the Anglo-American Bridge Project, currently starring Kevin Spacey in “Richard III” in London. Might the RSC ever entertain hiring a director like Sullivan? The Shakespeare Theatre Company had great success, for instance, importing Jonathan Mumby, a onetime RSC man, to stage Lope de Vega’s “The Dog in the Manger.” It’s high time that we did the reverse and showed British Shakespeare more of the Colonies' strengths.

Shakespeare in the Park

Through July 30 at Delacorte Theater, Central Park. Visit .

Royal Shakespeare Company at Lincoln Center Festival

Through Aug. 14 at the Park Avenue Armory, 643 Park Ave., New York. Visit or .