The Tempest, Theatre Royal, Bath / The Illusion, Southwark Playhouse, London / Soul Sister, Savoy, London

A naff spectacular with a strangely familiar storm was only saved by some superb acting

Some of the aristocrats shipwrecked on Prospero's isle in The Tempest hear invisible sprites singing sweet airs that delight and hurt not. Others hear barking, as if demonic hounds were at their heels. The castaways also see a banquet, like a mirage, laid out before them by fantastical creatures who vanish into thin air, replaced by a foreboding harpy. Shakespeare's late romance is always somewhat hallucinatory.

Surely, though, these mind games – played by the magus – shouldn't be accompanied by a severe case of déjà vu? Apologies for backtracking but last month, at the Edinburgh Festival, I cheered the theatrical brilliance of the hurricane in Ariane Mnouchkine's Les Naufragés du Fol Espoir – evoked with a vast, thrashing mainsail, thunderous drums, and the witty sight-gag of crouching actors flapping others' coat-tails.

A week later, how does Adrian Noble stage Prospero's storm at Bath Theatre Royal? Erm, with those same devices – and less skill. This is obviously coincidence or appreciative homage. Noble first staged this Tempest (in San Diego) in mid-2011, not in 2010 as suggested in the programme notes. Mnouchkine's production premiered (in Paris) in 2010.

Worse, Noble – a former head of the RSC – lets this show degenerate into a naff spectacular. Some of his English cast rise above this, but designer Deirdre Clancy's vaguely Far Eastern costumes look inauthentic. Mark Meadows' Ariel is, surely, the love-child of Johnny Weissmuller's Tarzan and Zandra Rhodes, his bare midriff and eyelids streaked with blue powder-paint. Shaun Davey's score is cheesy and obtrusive too.

At least Noble strongly highlights the theme of revolutionary emancipation. Fine clowning is supplied by Mark Hadfield as the booze-sodden upstart, Trinculo – covering one eye to stop himself seeing double. Tim Pigott-Smith's Prospero has gravitas and ire. Unlike Ian McKellen's (wholly unShakespearean) portrayal of the wizard in the Paralympics' Opening Ceremony, Pigott-Smith struggles to let his daughter go, even to her new love, Ferdinand. Mark Quartley transforms this normally wooden role into an over-whelmingly touching portrait of youthful ardour and resilience. He steals the show, in a totally wonderful way.

Written in 1636, The Illusion was Pierre Corneille's answer to The Tempest. In a dark cave dwells a magician called Alcandre who, we're told, has the power to raise storms and read minds. A father, named Pridamant, craves to know what has become of Clindor, the son who fled his strictures 10 years ago. Alcandre conjures up apparitional scenes for Pridamant, showing his offspring reduced to the status of a manservant but wedding a lady of rank whom he was supposed to be courting on behalf of his vainglorious master.

The Illusion is a teaser, like a Chinese box, compiled of layer upon layer of pretending. Alcandre's magic can, like Prospero's, be seen as a metaphor for the art of theatre-making. Moreover, within the core story of Clindor's adventures, reality and truth become increasingly elusive. Ultimately, we are led to understand that James Clyde's Pridamant has been watching actors playing a troupe of actors (or rather a mirage of a troupe of actors) who have, in turn, been depicting characters who have proved startlingly inconstant. If you believe Alcandre, that is.

Given all that unreliability, it would be foolish to moan that Tony Kushner's adaptation – staged by Seb Harcombe – isn't strictly The Illusion as we know it. Theatregoers unfamiliar with the original might well be surprised to learn how divergent this version is. Kushner has cut whole scenes, and invented a hunched lad, Daniel Easton's Amanuensis, who's kept in thrall by Alcandre (who is also a sorceress, portrayed with icy elegance by Melanie Jessop). But who's complaining when Kushner has enriched the drama with extra twists and darker psychological depths. Moreover, his freely inventive poetic dialogue is bewitching: vivid in its imagery, baroque in its eloquence, and more philosophically searching than Corneille.

Harcombe's production, in exquisite, ghostly, period costumes, also showcases the talents of recent graduates from Rada (where the director teaches). More work needs to be done on class accents, but Shanaya Rafaat is electrifying as a jovial maidservant who, when her romantic hero proves to be a gold-digging Lothario, mutates into an avenger with the hair-raising ferocity of a Medea.

The pop star Tina Turner, by contrast, seems to have had the patience of a saint, enduring her guitar-twanging husband Ike's serial adultery and violent temper for years. In the mid-Seventies, apparently with the help of Buddhist chanting, she found the strength to break free and became an icon of rocking feistiness.

The jukebox biomusical about her, Soul Sister, transferring from Hackney Empire to the West End, has a skimpy script disguised by Bob Eaton and Pete Brooks's slick staging, with video projections styled like a graphic novel. Crucially, Emi Wokoma does a rip-roaring impression of Tina, blasting out "River Deep, Mountain High" and two dozen other hits. But, the band is so loud that my eardrums were sore by the end: sweet airs that delight but hurt a bit.

'The Tempest' (01225-448 844) and 'The Illusion' (020-7407 0234) to 8 Sep; 'Soul Sister': (0844 871 7687) to 29 Sep