Two rip-roaring full-length premieres. The Royal Opera House is rather hogging the limelight – and both the X-rated Anna Nicole and Monday night’s family-friendly Alice (Alice’s Adventures in Wonderland, to give it its full title) are sure-fire hits with their audiences. The reception for the Royal Ballet’s offering – Alice is its first new full-length creation for two decades – was every bit as ecstatic as that lavished on Mark-Anthony Turnage’s opera and, in Lauren Cuthbertson, we had an Alice whose on-stage presence was always captivating, if not as compelling as Eva-Maria Westbroek in her remarkable portrayal of Anna. And Alice, like Anna, is on stage virtually throughout.

James Jolly has written perceptively about Anna Nicole, but I have my doubts about its long-term durability. Extravagantly entertaining though it may be, it is, I think, very much a piece of – and for – our time. Alice, on the other hand, is a timeless work given a treatment that takes full advantage of 21st-century techniques. The worlds of film, digital technology, burlesque and dance come together to create a fabulous entertainment. True, it lacks any compelling narrative thread, but Lewis Carroll’s strange and wonderful characters treat us to a succession of dances and sketches, some riotously successful, that never fail to engage with the audience.

We begin at a summer afternoon garden party in Oxford in 1862, where Lewis Carroll is entertaining the children. Alice’s friend Jack, the gardener’s boy, is dismissed in disgrace by Alice’s stern mother for eating a jam tart. Carroll comforts Alice by taking her photo (with an 1862 camera, mind), emerging from behind the camera as the White Rabbit. He vanishes, Alice follows and falls…and suddenly we are in the cinema watching Alice fall and fall…and fall. And it’s all very clever as, by mixing media, Alice become convincingly tiny when she succumbs to the temptation to “Drink Me” and moments later becomes a walls-busting giantess.

The array of Carroll’s characters that populate Wonderland perform their turns with relish and, in many cases, considerable aplomb, Steven McRae’s tap-dancing Mad Hatter just one of many enthralling cameos. In Wonderland, Alice’s mean mum has become the “off with their heads” Queen of Hearts – Zenaida Yanowsky is a nightmare come true and her wicked pastiche of Petipa's Rose Adagio from The Sleeping Beauty brings the house down. And I mustn’t forget the Cheshire Cat, truly a creation of our multi-media age.

Edward Watson brings all his consummate flair to the dual role of the White Rabbit and Carroll himself and Sergei Polunin soars effortlessly as Jack-turned-Knave of Hearts. At the heart of it all is Cuthbertson’s touching and empathetic Alice. The girl from Devon is the Royal Ballet’s youngest female principal and only recently returned to the stage after illness sidelined her for the whole of last season. How she has come of age and what a role she has created!

Barry Wordsworth conducted Joby Talbot’s massive new score, replete with shofar – a first, I suspect, for Covent Garden – with relish. It’s mellifluous, it flows and it’s the perfect foil for Christopher Wheeldon’s choreography, which is always full of fascination – and fun.

And, in the end, fun is what this new ballet is. The stage was strewn with yellow daffodils and red roses at the end – several dancers all but slid to the floor during their curtain calls – and one felt we might have seen something that will have a rather longer shelf life than the Royal Ballet’s last attempt at a new full-length work.

Forecasting the future is fraught and it is highly unusual for two such high-profile new works as Anna and Alice to have come to Covent Garden at the same time. For two weeks, everyone has been talking about Anna and tickets are harder to come by than gold dust. I fancy, though, that of the two works Alice may be the one that better stands the test of time.