Sinead O'Connor, St John-at-Hackney, London Skrillex, Academy, Bristol

The often controversial singer packs an emotional punch as she lets her powerful voice rip in an east London church

Performing in a church is, for Sinead O'Connor, surely the very definition of "conflicted".

At least, it is if you're hazy about the timeline. An outspoken critic of established religion in her early career, the singer knew whereof she spoke, following a troubled childhood spent in and out of Catholic asylums. Her controversial stance reached a peak in 1992, when she caused uproar in America on Saturday Night Live modifying a Bob Marley song to accuse the Roman Catholic church of child abuse.

By the end of the 1990s, she'd been ordained as a priest – Mother Bernadette Mary – in an independent Catholic church. Of course, being a Christian and being opposed to the established church are not mutually exclusive, but her apparent conversion was an eyebrow-raiser. The religious content of her work has since increased. She released an album with the title She Who Dwells in the Secret Place of the Most High Shall Abide under the Shadow of the Almighty (a reference to Psalm 91), containing Latin hymns. Another album, Throw Down Your Arms, was based on Rastafarianism, and her most recent effort, Theology, consisted largely of religious songs. Her new album, Home, is cut from the same cloth: this show's opening track contains the words "I played the part of Jesus".

Tonight, she's a replica of the Sinead who first rose to fame, with one crucial difference. Her head shaven with just the slightest hint of a Travis Bickle on top, she wears teetering stilettos, leatherette leggings, a black basque and an Eighties success coat. But if the Rastafarian wristband isn't a giveaway that a lot has changed, then her tattoo is: an enormous chest-piece of Christ in a tangle of thorns.

Even leaving religion aside, Sinead O'Connor was never the easiest persona to warm to: an icon, whether by accident or design, of the solipsistic student-feminist Eighties left. Clare Grogan's depiction of Sinead as "Niamh Connolly" in Father Ted, portraying her as a joy-hating martinet, seemed all too believable. That said, perhaps she's developed a sense of humour in her old age: another new song has the line "He looks just like me, the bald-headed baby...".

One thing she always had, of course, was one hell of a voice. O'Connor had the ability to flit effortlessly between that Celtic yodel and a startlingly pugnacious blare. And she's still got it, even if her showstopping version of "Nothing Compares 2 U" has lost some of its power now that Prince has reclaimed the song as his own.

Now returned from temporary retirement after developing fibromyalgia, the noise she makes with her fully electrified six-piece band consists mainly of mid-paced MOR rock and sonorous, atmospheric folk, with nothing to frighten the horses. But suddenly, something extraordinary happens. O'Connor dedicates "I Am Stretched on Your Grave" to Wales football manager Gary Speed, news of whose death had filtered through earlier in the day. The room is so silent you can hear a pen click (and, I'm ashamed to admit, it's mine) as she delivers an utterly spellbinding a cappella rendition of the song. The explosion of applause at the end is as much for Speed as it is for Sinead.

The cognoscenti may turn up their noses, but there's something about fast-rising electronic producer Skrillex that has transcended factional divisions, uniting rock fans and dance kids with fiendish effectiveness.

Skrillex is the alter ego of Sonny Moore, former singer in Florida emo band From First to Last, who has evidently undergone a conversion every bit as dramatic as Sinead's. With his long hair and nerdy glasses, he may look like a live-action role-play aficionado plucked from the local metal club, but he specialises in physically irresistible electro with bass so thunderous it loosens your fillings. He's also unafraid of crowd-pleasing cheese: I do a double-take when he throws in snatches of Naughty by Nature's "Hip Hop Hooray" and Kriss Kross's "Jump".

Even though I have it on good authority that the set list changes every night and he mixes it up live, it's questionable whether Moore's actually doing anything other than pressing "play". Backed by stereotypical "rave" visuals, he stands behind a trestle table containing CDJ decks, a laptop and a couple of other gadgets, and spends much of the time hands-off, clapping and cheerleading.

The reaction, regardless, is phenomenal: save for precious breakdowns between the beats, the balcony bounces unsettlingly. Suddenly, everything stops. For the Benny Benassi/ Gary Go collaboration "Cinema", arms are thrown around strangers' shoulders and there's a sentimental singalong to the lines "I could watch you for a lifetime/You're my favourite movie/A thousand endings/You mean everything to me". The world's first dubstep power ballad?

Even if you have no frame of reference for comparison, something about Skrillex's shtick is working, and kids you'd normally see at rock festivals are going nuts alongside kids you'd normally see at raves. As history has shown, that's a devastatingly lucrative trick if you can pull it off. Love it or hate it, Moore's got the skrills to pay the bills.

Next Week:

Simon Price gets his poodle on with Def Leppard and Mötley Crüe

Pop Choice

It's a clash of the radio stations as Capital FM's Jingle Bell Ball brings JLS, Jessie J, Ed Sheeran, One Direction, Emeli Sande, Wretch 32, The Saturdays and others to London's 02 (today); and XFM Winter Wonderland brings Chase & Status, Nero, Ed Sheeran (again) and The Big Pink to the Apollo, Manchester (Mon).