So, what's to choose between them? The Bolshoi has novelty on its side - its last visit to London was in 1993 - but it also has a reputation to restore. A candid Channel 4 documentary which showed the company grubbing for dollars in Las Vegas rubbed off much of the gilded glamour it once heldfor us. There is a new director at the helm who claims to have brought the dancers back up to scratch; there is a potentially lethal lawsuit in the offing (from a vengeful ex-director with copyright claims); and there is the thrill of seeing a stageful of leggy, swan-necked, physically implausible human beings with a direct link to ballet's glorious past.
Bayadere was a baffling choice in some respects. It has far and away the silliest plot of all the Russian classics. But it does offer an excuse to blow the costume budget sky-high as well as field a mammoth cast. "Bolshoi" means big, and it is. Mud-smeared fakirs, jewelled temple girls, frenzied hula-dancers and a pneumatic bronze buddha are but a small sample of its exotica. I could have done without the intendedly comic chorus of blacked- up slaves. Sometimes there is an argument for tampering with the classics. Slash and burn, in this case.
A more important focus in Bayadere is the love theme (an Indian warrior casts aside a faithful temple girl to marry a rajah's daughter) but its potency here was undermined by a Solor of questionable sex. Imagine The Artist Formerly Known as Prince in a lilac bikini-top. Nicolai Tsiskaridze, a dancer of gazelle-like elegance, is a whizz with his spins and leaps, but I never for one minute believed he loved either of the women. And their celebrated cat-fight, which culminates in the bayadere threatening to stab the bitchy princess, was completely fudged. Had I not known the plot, I would have missed the dagger entirely.
What keeps this work in the repertoire is Act III's "Kingdom of the Shades", with its dozens of gauzy ballerinas arabesque-ing in a moonlit snaking line. And here the Bolshoi really is the business. For once, the steep- raked descent does suggest the Himalayas, and the ghostly maidens perform a trance-like processional with an artistry that made my heart stand still. It was worth sitting through two hours of variety-show guff for this 10 minutes of tutu'd perfection.
That immaculate schooling shone through again on Thursday, when the same company gave its Giselle. As the ranks of spectral Wilis began to muster for their assault on Hilarion, that famous unbroken horizontal of raised legs and accusing fingers had a ferocity that would make an exorcist blench.
Terrifying, those women were. And oh my, what fine dancing we had from the two principals, particularly from Svetlana Lunkina, aged 18. In Act I she was a veritabledaisy of freshness and grace whose loves and griefs and shynesses and joys we lived through second by exquisite second. As a spectre in Act II, she was icy, detached, dazzling. I've not seen that weird, awkward, whirling-on-the-flat-of-one- foot sequence danced so fiercely, so fast, nor as such a thing of beauty. As an image of life leaving its mortal coil it was unforgettable.
And yet, for me, the ballet event of the week happened elsewhere, at Sadler's Wells, in the hoary Peter Wright production we've seen many times before. Sylvie Guillem has twice Lunkina's years, yet her portrayal of a betrayed young thing was every bit as captivating, and more. With Guillem, it's as if everyone else is acting and she is the original article. In Act I, the peasant girl who loves to dance doesn't just appear on stage dancing. She comes on, registers an empty space, and makes us feel her irrepressible desire to fill it - a small theatrical miracle of reflex and nuance. I clutched the edge of my seat throughout. At times, I softly wept. Keep her close, Royal Ballet. Sylvie Guillem is your crown jewel.
Bolshoi: Coliseum, WC1 (0171 632 8300) to 7 August; Royal Ballet: Sadler's Wells, EC1 (0171 863 8000) to 31 July