Ooooh, it's a drama war between the BBC and ITV1! On the same day, in the same time slot, we have He Kills Coppers v The No 1 Ladies' Detective Agency! How flattering of the big broadcasters, to presume that, instead of spending Sunday night looking for talking cats on YouTube, what we really want is some classy drama, which we will appreciate, because we are cultured, and dead posh, and eat sandwiches with a knife and fork. Off a plate.

As it turns out, you don't need to be posh at all for The No 1 Ladies' Detective Agency. You could be eating cornflakes off the floor with your face for all it demands of you. Whenever you see the credit “adapted by Richard Curtis”, you know you are unlikely to wander into an hour of killer replicants, Jungian dream sequences and random narrative time shifts. And, sure enough, The No 1 Ladies' Detective Agency is, like the book that spawned it, “charming”. It's all “lovely shots of giraffes in the bush” this, and “people quoting old African proverbs at each other while drinking rooibos tea on the veranda” that. And endless amounts of “Jill Scott as Precious Ramotswe, being a warm-hearted, maverick woman” the other. It might as well be called the “We Love Jill Scott's Gentle Eyes and Indomitable Spirit Show”.

In fact, if you put aside the faintly incongruous side-plot about witchcraft and child sacrifice - I know! How unexpectedly and randomly dark! - then The No 1 Ladies' actually plays out like a Botswanan version of The Vicar of Dibley. Here's the “sturdy” Precious Ramotswe (Scott), breaking with all traditions and taking on a job (detective) that was previously the employ of men. Here's her slightly odd, socially maladroit sidekick (Anika Noni Rose as Grace Makutsi), whom she takes under her wing. Here's the village she moves to, full of both a) lovely scenery and b) eccentric, handily plot-generating local characters.

No wonder Curtis chucked his hat into the ring to adapt the book. Once the proper series starts - this is just the pilot - he can dig out a couple of old scripts, scribble out “Dibley” and “labrador” and replace them with “Gaborone” and “lion”, and then take the rest of the afternoon off. And why not? I like Curtis. I like his cheery films that believe in love. It's no crime to make warm, accessible, prime-time dramas - although from the amount of sniffy comments people have been making about The No 1 Ladies' Detective Agency, you'd think it was. And besides, it's scarcely like the pappy, artless Wild at Heart, but with some mysteries. This is a prime-time drama with an all-black cast, and cinematography by the late Anthony Minghella. And it also has the year's best cameo so far - David Oyelowo as a musky, jivey, priapic stud-stoat practically writhing off the screen with glee. He needs to play a hyperactive sleazebag in tight trousers more often. He has a great talent. And the ladies will know what I mean when they watch it.

However, if you can bear to leave the warm, bath-like ease of The No 1 Ladies' Detective Agency, then do flick over to the categorically superior He Kills Coppers on ITV1 - not least for its opening monologue from Rafe Spall, which might be the most Cockney thing that's ever happened. I can't tell you how excitingly he delivers the phrase “Not that I gave a shit - I'm a bloody good thief taker, and I knew where I was going.” I've been trying to crowbar a poor impression into conversations all week. The children have taken it very badly.

He Kills Coppers is superior, feel-the-lining-on-this stuff - bafflingly good for ITV1. Spall is a low, sure, hypnotic note - a cocksure, slightly bent rookie detective in 1966; all fags, Brylcreem and tarts. The great casting continues with the mesmeric Kelly Reilly as a prostitute who is both fragile and brassily capable: a certain kind of working-class girl you got in “the olden days”, who was a feminist before feminism was invented. Alas, the retro detailing seems to extend to the sound-mix, which seems to have been done through a single mono loudspeaker in 1966 - whole swaths of dialogue are inaudible. But if you have subtitles on your TV, this is definitely the winner of the Sunday Night Drama Stand-Off.

The No 1 Ladies' Detective Agency, Easter Day, BBC One, 9pm; He Kills Coppers, Easter Day, ITV1, 9pm

Editor's choice

• The 100 Best Films of the Decade
• 70 facts you didn't know about Marvel
• The 50 Biggest Movies Of 2010