When Haydn completed his Six Quartets, Op 50, in 1787, they triggered a Europe-wide bidding war among music publishers. As well they might: this was Haydn’s first full-scale set of quartets since the groundbreaking Op 33 and his meeting with Mozart. There isn’t much of Mozart in Op 50. But there is, unmistakably, a new freedom – an expansive, sometimes explosive readiness to explore wherever Haydn’s imagination took him, from the fire-and-ice fugue that ends No 4 to the string-crossing high jinks of the so-called Frog Quartet, No 6.

In other words, this is music that contains multitudes – open to limitless interpretative possibilities. The very packaging of these releases from the Zaïde and the period-instrument London Haydn quartets illustrates just how different those possibilities can be. The London set is beautifully produced in the best Hyperion tradition, complete with 18th-century oil painting on the cover and a scholarly essay by Richard Wigmore. The Zaïdes’ cover photo shows the quartet’s young members looking like they’re having the time of their lives.

They play like it too. The London Haydn Quartet’s cellist Jonathan Manson begins No 1 by laying down a steady, level pulse over which his colleagues elegantly place Haydn’s opening phrases. Juliette Salmona, for the Zaïde Quartet, is more crisp, with a distinct swell that isn’t indicated in any edition of the score (the Londons play from the 1787 Artaria edition) – but which you might feel is implied by what happens next. Violinist Catherine Manson of the Londons dances skittishly down her triplets into the first forte; the Zaïdes’ Charlotte Juillard plunges in like a bird of prey.

That exuberance and drama defines the Zaïdes’ set. At times it can seem almost too much; listen to the lip-smacking relish with which Juillard brings out the outrageous sopra una corda slides that Haydn writes into the main theme of the finale in No 5, or the way the players, ornamenting extravagantly, almost seem to tumble over each other from 2'10" onwards in the second movement of No 4. Disruptive? Yes, but imaginative, unexpected, and part of a conception that makes every ornament and bit of passagework part of a vivid, forward-moving conversation. The Zaïdes do delicacy too: listen to how naturally they place the quiet final notes of the first movement of the Frog. Recorded in lively close-up, these performances are fun but never throwaway.

If the London Haydn Quartet’s recorded sound is slightly more distant, that complements their performances, which are civilised, carefully prepared and spacious to a T. Unusually, they observe all the printed repeats in the outer movements, so whereas the first movement of the Zaïdes’ No 2 lasts 7'54", the Londons’ comes in at a positively Wagnerian 12'16". It doesn’t feel particularly vivace, either; you get the sense in outer movements throughout the set that the players are reining in their imaginations for long stretches, the better to release them second time around. That yields imposing results in the famously intense F sharp minor Quartet, No 4; elsewhere it can all feel a little – well, chaste is the word that came to mind, though the pay-offs (such as their fizzing, high-speed humour in the finale of No 3) often justify the wait.

These are stylish, faithful accounts of these six great quartets, and if you’ve been collecting the London Haydn Quartet’s ongoing Hyperion cycle, you needn’t hesitate (those seeking an earthier period-instrument version might try the Festetics Quartet on Arcana). But it’s the Zaïdes’ set that I’ve found myself returning to for sheer pleasure – and a vision of Haydn as explorer, innovator and entertainer that simply dances for joy.