Last night's viewing - Death in Paradise, BBC1; Jamie's Great Britain, Channel 4

As soon as I've solved this case and got my luggage, I'll be on the next plane home," Richard Poole told his new colleague in Death in Paradise. "I can't think why they've sent me here." I've got an idea why, though. They've sent him there because the BBC wants something a bit Doc Martinish for Tuesday evenings, and it thought it would be a bit too obvious if it commissioned a drama about a grumpy, uptight doctor in a Cornish village. So, instead, we've got a grumpy, uptight detective inspector on the Caribbean island of Sainte-Marie, where the locals look as if they'll be just as characterfully eccentric as the inhabitants of Port Wenn and the metropolitan prejudices of the newcomer are likely to be confounded in a virtually identical manner. One understands (with a sinking heart) that DI Poole is here to have his shirt unstuffed by easy-going types who appear – in their characterisation – just a whisker away from the sunny hedonists of the Lilt adverts.

Not that there's any real discrimination here, because everyone's a caricature in Death in Paradise, their essential qualities semaphored with a brutal simplicity. We know that Poole is a stickler because he makes appointments in digital time ("I'll call you at 6.01, Daphne") and we know that he's out of his comfort zone because he keeps going on and on about the temperature. We also know that he's not real, because despite wincing every time he looks at the sun, he doesn't even loosen his tie or take off his jacket, hardly a shocking breach of protocol if your luggage has been mislaid and you claim you're expiring because of the heat. Like the goat in the police cell (a genuinely condescending touch of local colour), Poole's buttoned-up demeanour is just a cipher flag.

The only rational explanation for his behaviour, in fact, would be that he's an idiot. But we know we can't just conclude that and have done with it, because he's the hero of a detective series, so it won't be long before he's staring sagaciously into the shrubbery and coming up with some brilliant aperçu. The mystery in this case involved a classic locked-room enigma, with a light sprinkling of other canonical detective plot devices (the clue hidden in plain sight, the law-enforcer who turns out to be a law-breaker) and it was worked through with a mechanical, box-ticking efficiency. We had one of those moments where a falsely accused suspect breaks down and blurts out her real secret ("No! I didn't kill him! I loved him!") and a final exposition that appeared to have been cut-and-pasted from a Poirot novel: "But in this case," announced Poole, "nothing has been what it seems."

What really irritates, though, is the apparent belief that nothing needs to make sense as long as it's notionally comic. The closing shot – in which we see Poole effortfully dragging his suitcase through the surf-line to the shack in which he's been billeted – is a good example. Since we've already seen him entering this building earlier, after being driven to the door in a police Land Rover, the only conclusion is that he's deliberately struggled down the beach in order to appear as awkwardly out of his depth as possible. It's a transparent fake, in other words, as beaded with sweat as Poole himself. It's at this point that someone will usually say, "Oh, come on. It's just a bit of undemanding fun." It isn't the programme that's undemanding, though. It's us and if we don't insist on more then we don't really deserve better.

Jamie's Great Britain offers a very different image of the British – not hidebound, anal and stuffy but with a magpie appetite for new experiences and new tastes. He trundles around the country in a reconditioned army van, revealing the cosmopolitan history of supposedly traditional dishes and cooking up his own variations. And, unlike Death in Paradise, it won't leave you with an overpowering feeling of dyspepsia.