Art is not a competition. Since, however, this is the second Much Ado in five days, comparisons are inevitable. And, while Jeremy Herrin's version at Shakespeare's Globe has many admirable qualities, this West End revival is 20 minutes shorter, more socially specific and much sexier. The pairing of David Tennant as Benedick with Catherine Tate as Beatrice is a marriage that, if not made in heaven, is certainly cemented by television and pays off superbly.

They are helped by Josie Rourke's decision to set the action in early 1980s Gibraltar: a world of crisp navy uniforms, clear class distinctions and high-spirited post-Falklands partying. It provides a perfect excuse for leisured officers to trick Bea and Ben into falling in love. It also lends plausibility to the main plot in which Hero, on her wedding-eve, has supposedly betrayed Claudio with another man. Rourke here interpolates a whole new hen-party scene in which we see Hero's maid, wearing her mistress's wig, enjoying some noisy rumpy-pumpy in disco-club darkness. One of Shakespeare's most clumsy plot devices suddenly acquires credibility.

Rourke has made other changes such as endowing Hero's dad, Leonato, with a wife instead of a brother: a deft touch since it makes Hero's disgrace even more disruptive to the family. But, while I like the production's colourful circumstantial detail, one of Rourke's ideas misfires. Seeking to show Claudio's penitence over his mistreatment of Hero, Rourke has him attempting suicide at her tomb until she makes a ghostly appearance. I get Rourke's drift but it kills stone dead the later moment when Hero is discovered to be alive and well.

Down the ages people have always gone to this play to watch the verbal sparring of Beatrice and Benedick which anticipates 1930s Hollywood screwball comedy; and here Tate and Tennant give just the right suggestion that their byplay is the product of some past bruising encounter. Tennant is especially good at showing Benedick's transition from the self-conscious madcap of the officers' mess into a man capable of love. He makes his entrance in a golf-buggy, dons a Lily Savage wig and tight skirt for Leonato's party but is hit amidships when he learns that he is adored by Beatrice. The great comic moment in Tennant's performance comes when, flinging his arms wide to the heavens, he declares: "I will be horribly in love with her."

Tate gives an excellent account of Beatrice as the kind of larky, high-spirited woman who uses her wisecracking gifts as a defence against emotional engagement: significantly, while Benedick turns up at Leonato's party in female attire, she comes dressed as a man. I'd only beg Tate to resist a textual change made, presumably, out of political correctness. In the gulling scene Shakespeare's Beatrice says of Benedick: "I will requite thee, Taming my wild heart to thy loving hand." Tate substitutes "with" for "to" to soften the note of submission: totally unnecessary since there's no danger of this sparky couple ever being anything other than sexual equals.

They are at the centre of a supremely well-cast production in which Elliott Levey as a closeted Don John, Tom Bateman and Sarah MacRae as a vibrantly attractive Claudio and Hero and John Ramm as a hamfisted Dogberry all make their mark. Lucy Gaiger's costumes, combining naval whites with snazzy civilian colours, add greatly to the gaiety of an evening that suggests the Tate-Tennant partnership should be pursued. Why not try their hand at Restoration comedy or Coward's Private Lives?

Until 3 September. Box office: 0844 482 5120