Madonna, Hyde Park, London / Wanda Jackson, Islington Assembly Hall, London

There's no contradiction between being a dreadful human being and a fantastic pop star. It's just a shame that Madonna, who sealed her status as the former six years ago by wearing a coat made of 40 factory-farmed chinchillas, is so rarely the latter.

The one-woman chinchillocaust brings her MDNA tour to London – oh, the desperate controversy of that title – and it goes off with a whimper, not a bang. But the reason has nothing to do with her age. Face facts: whether it's achieved in the gym or the surgery, Madonna has a damn fine body (and strips down to thong and bra to prove it). If Madonna isn't sexy, it's not because she's 53. For a woman who sings – or mimes – about sex, she's always made it seem like cold, hard work, all Pilates and no passion.

And yes, her face may be morphing into Priscilla Presley, but with Madonna's wealth, we'd all get botoxed too. And who cares if "Express Yourself" is the one thing her face is unable to do? That song, ironically, features the night's most eyebrow-raising moment (a tricky feat for a frozen forehead). Madonna's smart enough to steal back from the stealers, and the no-singing, all-dancing MDNA show's opener has a Vatican-gothic aesthetic that feels straight out of Haus of Gaga, until you remember that Madonna got there first with "Like A Prayer".

So far, so innocent, all part of the cycle of pop. But later, during "Express Yourself" – famously plagiarised by La Germanotta on "Born This Way" – Ciccone inserts the chorus of her junior's hit, before repeating the words "she's not me!" with pointed venom. Four times.

She's right, but for all the wrong reasons. Unlike Lady Gaga, Madonna has always had a head-smashingly banal idea of what it means to be "edgy", and tonight it means getting kidnapped by terrorists on trapezes and shooting hooded assailants with an AK47. The MDNA setlist is heavy on new material, with echoes of the old. "Girl Gone Wild" contains homeopathic traces of "Material Girl", just as the corset she wears for "Vogue" echoes her famous cone-bra. The main musical innovation is her belated discovery of gypsy folk (see revamped "Justify My Love").

"I like to live dangerously", she boasts, as she sprawls on the catwalk, freshly mopped of rain by flunkies. But if the Chinchilla Killa has proved one thing tonight, it's that there's a fine line between "dangerous" and dull.

If you saw Wanda Jackson in the street, with her big black bouffant, emerald eyeshadow and bling, you might take her for a sweet old lady. But within five words of "Riot in Cell Block #9", there's no mistaking that voice. A hellcat rasp rivalled in its day only by Brenda Lee, it's why the Hall of Fame inductee is still known as the Queen of Rockabilly and has a street named after her in Oklahoma City. And it's the reason why, with the excellent Jack White-produced The Party Ain't Over, she's become the oldest woman with an album in the Billboard charts, deposing – as she takes great pleasure in telling a packed theatre – Mae West.

Jackson's career has followed a familiar trajectory for a Fifties rock'*'roll star: turned to Country in the late Sixties, discovered Jesus in the early Seventies, only to rediscover rock'*'roll in her later years, then find herself rediscovered by successive cool cats from The Fall to Adele, who took Wanda on tour and admitted that Jackson's slinky, sultry "Funnel of Love" inspired "Rolling In The Deep".

Jackson blazed the trail for generations of she-rockers. She's been recording for 58 years and touring for 56, but there's only one story everyone wants to hear. In her late teens, not turned off by his yellow sports jacket and pink Cadillac, she dated Elvis. And it was Presley, she says, who persuaded her to sing rock'*'roll.

She returns the compliment by covering his "Good Rockin' Tonight" and "Heartbreak Hotel". She also takes on Johnny Kidd & The Pirates' "Shakin' All Over" and Amy Winehouse's "You Know I'm No Good", but the real thrill is hearing her own hits. In "Fujiyama Mama", released just 14 years after the end of the Second World War, Wanda outrageously compares her loving prowess to the atom bomb: "I've been to Nagasaki, Hiroshima too/The things I did to them baby, I can do to you!" Amazingly, it went to No 1 in Japan.

Jackson's been struggling with a cold all week, but still carries off the acrobatic yodelling in "I Betcha My Heart I Love You", and makes it through to her signature finale "Let's Have a Party". They don't call her Leather Lungs for nothing.