Jake or Dinos Chapman, White Cube Mason's Yard and Hoxton

It begins in a so-so fashion. The ground-floor gallery at White Cube’s Mason’s Yard features a sea of Constructivist sculptures on plinths. These are made from bits of torn cardboard and loo rolls, sloppily painted. Jake and Dinos Chapman love corny art jokes, but this gag feels like it’s already a little flat. And I’m disappointed to be disappointed. Chapman exhibitions are always something to look forward to, and I was looking forward to this one, especially since they had in mind a game. And the game in this instance was that they had worked independently for the first time - in separate studios and unseen by the other - and you’d have to guess who’d done what.

This is, in fact, impossible to do. One is tempted to think the stuff that you like, the work that’s especially witty, has been made by the theorising brains of the pair. That’s Jake, the older brother and the one who does most of the talking. But articulate artists don’t necessarily make the best, the most intuitive artists, and since Jake and Dinos have always collaborated they have, presumably, absorbed the ideas, modes and methods of the other. They are like inseparable art twins.

Disappointment doesn’t last long, however, and perhaps that's my initial reaction because I always expect a lot from these two. Their work has a wow factor: it’s startling and surprising, and it also makes you laugh. Their work is a blast. But on a deeper note – though what’s deeper than finding humour in dark matter? – they have the talent to deliver rich, layered work. They are clever, but sometimes it’s difficult to work out whether they’ve been too clever by half or just puerile.

Downstairs things heat up. The basement gallery is crowded with tar-faced Nazis, charred-looking and flayed, each with frozen, skull-like grins and pop-eyes (pictured right). Their uniforms are immaculate and their armbands carry not swastikas but smiley faces. They stand, they point, they peer at the artwork. A pair are copulating. The Nazis are gathered round more constructions, this time referencing earlier Chapman works featuring faux-primitive monkey sculptures. Two tall Richard Serra-alikes are painted in black, and stuffed birds perch atop them and eyeballs are glued to their surfaces. But it's the Nazis who've become the winning exhibits in this degenerate art show.

The etchings and collages lining all four walls are, as ever, exquisite. These always display such a dainty touch, but as usual they are of beastly things. On the back wall are some Goya etchings transformed with delicate, precise markings, and there are some which are almost blanked-out with black washes of paint (which Chapman has the feeling for Expressionism and which for anally precise mark-making?). To the right are some torn pages from a child’s join-the-dot book where an elephant has, naturally, a penis for a trunk. Visual gags and references abound, but guess what? There’s a real Brueghel on display in the darkened corridor of the stairwell – either by Pieter the Younger or possibly his less talented son. The made-over peasants are sporting ugly pike noses and ghoulish faces.

Over at Hoxton Square, I am tickled to see a group of small children gathered round one of the paintings – one of a series of muddy, faintly delineated canvases depicting children’s story-book scenarios. From the back the kids look amazingly real (main picture), but of course they are mannequins; these have duck bills and wolfish features (pictured left). The badges of their uniforms carry the school motto: “They Teach Us Nothing”. Are we, are children, morally improved by an encounter with art? The Chapmans laugh at such old-fashioned, humanist notions. Those sophisticated Nazis liked art, and just look at what's become of these little ones.

It’s hard to explain in words what makes a visual gag a success, though I’ll confidently state that the exhibition does end on a bit of a flat note upstairs. We find homely Catholic shrines defaced, the usual blasphemy shtick. A Madonna has had half the flesh of her face ripped off and the baby Jesus is spewing forth bloodied octopus tentacles. Still, there’s plenty here that will tickle and delight. As I said, the Chapmans are a blast. Best start off at Mason’s Yard.

• Jake or Dinos Chapman at White Cube Mason’s Yard and Hoxton until 17 September