What have a rock musical and a Donizetti opera in common? Not much, you might say, but seeing the new West End production of Hair at the Gielgud Theatre (with the cast imported wholesale from Broadway) and La Fille du Regiment at Covent Garden on successive evenings immediately before my recent holiday gave me an interesting perspective.

First, the performances themselves. I had missed this La Fille when the production was new, that now-famous occasion when the exceptional on-stage chemistry (as I can now judge from the DVD) of Juan Diego Flórez and Natalie Dessay had made it the hottest ticket in town. This time, with largely the same cast returning and Maurizio Benini again in the pit, I would make no such mistake. And I was not disappointed.

The opera is not one of Donizetti’s best. The jokes come thin and slow, and the music is for the most part the composer on auto-pilot. A star vehicle this is not, or if it is it’s an old banger. So production and ensemble have to be razor-sharp and in this, the Royal Opera score. Dessay and Flórez are the flag-wavers for an entire cast filled with vivid performers on their mettle – Ann Murray as the melodramatic Marquise of Birkenfeld, Donald Maxwell as her expostulating butler, Alessandro Corbelli as a rotund and immensely characterful Sergeant Sulpice. Flórez was delightfully eager of eye and of voice as the ardent Tonio. He is the soul of style, making the most of a freakishly robust but occasionally still narrow-sounding voice. Dessay, meanwhile could easily have had a second career as a clown, or a mime, such are her accomplishments as a physical actress. From her first entrance, busily karate chopping her ironing into shape, this was a performance of body, voice and mind. And Dessay managed to catch not only Marie’s stubbornness, as the adopted daughter of an entire regiment, but also her loneliness. Her performance, like the entire show, was agile, light on its feet, and very, very funny.

Hair is not especially agile. It tends to lurch from one rock anthem to the next with the loosest and least coherent of stories to hold them together. Essentially, a young New York hippie must decide whether, like his friends, to dodge the Vietnam draft or, as his father puts it, to face up to his patriotic duty. But really, beyond those bare bones, there’s not much point worrying about the finer points of the narrative. Perhaps it was seeing this the night after Fille, but it occurs to me that Hair is the Tristan und Isolde of musicals. I know, it sounds a ridiculous statement, but as you succumb to the outpouring of raw emotion through music, to the endless melodic momentum pushing you through to the poignant climax, by which time and despite the haphazard script you feel put through the wringer, it feels very much like that familiar Tristan effect. Let it wash through you, treat it as an opera, and you’ll find the emotional release.

Which is probably why, polished and likeable as this cast is, I preferred Daniel Kramer’s more consciously operatic staging for the little Gate theatre in 2005. This production sent me smiling into the night. Kramer’s had sent me reeling.

Theatre and opera meet also this month at Glyndebourne, where the Donmar Warehouse’s artistic director Michael Grandage has staged his first opera. Chatting to Grandage a few years ago just after seeing his momentous – and very operatic - staging of Schiller’s Don Carlos, I asked him whether he’d considered tackling Verdi’s opera. Or any other. He wanted to try opera, he’d replied, but wasn’t sure which. I suggested he take a look at Simon Boccanegra. In the event he’s plumped for Britten’s Billy Budd.

In Christopher Oram’s brilliantly atmospheric ship’s-hull set, Grandage keeps the action immediate and there’s plenty of detailed characterisation (clever, the way Captain Vere’s officers gradually became disillusioned with him). But the chorus sometimes leave him somewhat at a loss, often a tell-tale sign of a director new to opera – at their first entrance, for instance, how much more effective it might have been to have had them revealed already in the darkness around Vere rather then trooping in to take up their positions scrubbing the deck. More surprisingly, John Mark Ainsley’s beautifully sung Vere stops just short of showing the character’s complexity, a problem calling out for more detailed work with a director. Does it take an instinctive opera director to know how to work with a classical singer on text? Perhaps. The same is true of Phillip Ens as Claggart, but since one couldn’t make out very many of his words at all I’m not sure Grandage could have accomplished very much, for all Ens’s malevolent booming. I also find it strange that the production entirely ignored all traces of homo-eroticism, when it’s clearly there in the music.

The star on stage is Jacques Imbrailio’s Billy, sung with virile tone and the first Budd I have seen who realises the character’s crucial touch of vanity, one reason he is taken off guard by Claggart’s plotting. But Mark Elder’s conducting is the best reason to catch this show. He and the London Philharmonic play the score spare and taut. You can all but feel the sting of salt sea spray. One consequence of this approach is an absolute clarity through which the drive to Budd’s destruction is chillingly apparent.

A very fine Budd, then. But coming from the hyper-talented Grandage, just as with the Vere of the similarly blessed Ainsley, I’d expected just that little bit more.