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Public Enemy, The Dome, Brighton Tame Impala, Brixton Academy, London

The Enemy strike back – and not a moment too soon

When you're Public Enemy, everything is political. Even the water you drink to cool you down. "H2O is in danger if the world does not watch itself," warns Chuck D between sips, pointing at his plastic bottle and calling it "the oil of the future".

This has been an extraordinary year for PE. A quarter of a century since the rap radicals first scandalised America, they've found themselves undergoing an unexpected career revival. Following its prominent use in Channel 4's Paralympics coverage, great lost 2007 single "Harder Than You Think" had a sales surge that carried it into the UK Top Five, giving the band their biggest hit to date.

It'd be a thrilling piece of work in any era, Chuck delivering a typically apocalyptic call to arms over a backing track which uses a horn sample from Shirley Bassey's "Jezahel", but to hear it blasting from the radio in the second decade of this century is beyond beautiful. And, importantly, it means that when Public Enemy make a triumphant return to a town like Brighton, there's more to the show than pure nostalgia.

Inevitably, aside from the Paralympics-assisted smash, it's the Nation of Millions material that tears the roof off the Terrordome tonight: the pumped-up but paranoid manifestos "Bring the Noise" and "Don't Believe the Hype", the kettle-whistle craziness of "Rebel Without a Pause", the Slayer-sampling rap-rock assault of "She Watch Channel Zero" and, above all, "Night of the Living Baseheads".

One thing that doesn't hinder them is age. Midway through a phenomenally energetic performance, Chuck reminds us: "I'm 52 and he's 53. You're looking at 105 years in front of you. So there's no excuse for rappers half our age to move so slowly." To reinforce the point, he does a hilarious impression of the saggy-arsed body language of a lackadaisical new-generation rapper.

Chuck and Flavor Flav do not walk alone. The Security of the First World – part private ninja militia, part dance troupe – still prowl the stage like a weirdly camp cross between GI Joes and The Temptations. And DJ Lord, long-established replacement for Terminator X, carries off feats of turntablism with "Smells Like Teen Spirit" and "Seven Nation Army" that ought to make any part-time DJ wear the name with shame. Present company included.

In this election season, Chuck is careful to clarify that while PE are pro-Obama, it comes with a hefty "but". With resignation, he tells us: "Every time you visualise the USA, you come back with a lower IQ in your head." It's true. But every time you remember that the same USA is capable of giving birth to an act like Public Enemy, you come back with a shining ray of hope in your heart.

Tame Impala feel like a band making the step up. It isn't clear exactly what Kevin Parker is trying to say, but it's something to the effect that last time he and his Perth fellow voyagers played the UK, the venues were smaller. Parker – limp, languid, lank-haired – cuts an unlikely figure as a rock hero, but his band is doing something very, very right.

With their second album, Lonerism, Tame Impala are sounding like the band MGMT decided they didn't wanna be any more: purveyors of heartbreaking melodies beamed down from a position eight miles high above the rest of rock, augmented by synth whooshes that go into interstellar overdrive at just the right moments.

The influence of The Beatles is obvious, with Parker's dart-shaped Rickenbacker and Dominic Simper's McCartney-esque violin bass, and the tripped-out beauty of "Feels Like We Only Go Backwards". But their least Beatles-based moment is also their best. Recent single "Elephant", built on a similar chugging nouveau-glam beat to Goldfrapp's "Train", is one of the singles of the year so far.

Parker is not a natural performer, but he's not without a sense of humour. When he announces "Right, dudes, this is a song off our first album", I swear he raises an amused eyebrow at the ostentatious cheers from a crowd who almost certainly only bought it a week ago.

Critic's Choice

Ariel Pink's Haunted Graffiti, critically cooed-over psych-pop clever-clogs from Los Angeles, plays the Illuminations season at York Hall, London (Fri). Meanwhile, turntable genius and hip hop pioneer Grandmaster Flash makes a one-off UK visit to the Casino Rooms, Rochester (Fri).