More than a century has passed since Rimsky-Korsakov wrote The Golden Cockerel, but time has not dulled its cutting edge. He intended the opera as a scathing satire of Russian autocracy after his country's humiliating defeat in the Russo-Japanese war. Even so, Dodon's kingdom exists at any time and place wherever the word ‘law’ has an exotic ring to it (to quote Dodon in Act I).

Although St Basil's makes an appearance in Laurent Pelly's production at La Monnaie, this is only a token Russian reference in an interpretation focused on the opera's universal import, with post-apocalyptic sets that give the opera no particular location. Anna Matison's Mariinsky production, by contrast, emphasizes the opera's Russian flavour, starting with Dodon's oversized crown, which looks as if it might have fallen off one of the St Basil's towers. What must have seemed like a fine comic idea was unfortunately pursued to the detriment of the music and action, since Vladimir Feliauer as Dodon evidently finds the crown so unwieldy that his delivery and gestures are impeded.

The mysterious Cockerel's piercing cries punctuate the opera and contribute much to our overall experience, but presenting the bird on stage is a challenge. At the Mariinsky, Matison (whose background is in cinema) chooses a non-naturalistic solution: the Cockerel is a hipster girl with a smartphone, taking selfies to give her followers an idea of the absurd kingdom she is visiting. To assist the audience, she wears a backpack in the shape of a cockerel. Pelly, by contrast, prefers to heighten the absurdity by portraying the cockerel itself in a naturalistic fashion: the costume is impressively designed, and the dancer inside does the best job possible in making authentic movements, jerking the head or strutting across the stage. This outsize and formidable mutant is clearly capable of inflicting lethal damage on Dodon, and at the end is the sole character remaining on a barren stage, the last survivor of a global catastrophe.

Another challenge is the Astrologer's part, which Rimsky-Korsakov intended for a rare tenore altino voice, although he stated that a tenor using falsetto would be acceptable. At the Mariinsky, Andrei Popov only breaks through to the highest register by shouting, which hardly fits his coolly sinister stage presence. At La Monnaie, Alexander Kravets's falsetto occasionally falters, but in this case, this minor weakness is compatible with the Dracula-like characterization of his role – unsurprisingly, he rises from the (un)dead at the end.

Matison's production is knowingly over-populated, over-burdened with objects and awash with extraneous interpretations. The hipster Cockerel, for example, befriends the Parrot, which was not intended as a stage character, but is merely represented by a cor anglais from the orchestra pit, and at the end, the liberated Parrot reincarnates as the new Cockerel, while the original Cockerel (who knows why?) turns into the Queen of Shemakha and runs away, aghast. The Queen of Shemakha proper (not the Cockerel), while trying to seduce Dodon, is supposed to awaken the interest of the commander Polkan, but in this production, she actually falls for Polkan herself – again, a change merely for the sake of a change. The costumes are amusing and bulky, vaguely referencing Larionov's costumes for Prokofiev's ballet Chout (1921). There is much hustle and bustle onstage, some of it quite meaningless, but it helps to pass the time for those in the audience who are not won over by the music.

Pelly's production makes a stark contrast, since it sits at the minimalist and monochrome end of the spectrum. His singer-actors are given all the space they need to act out their roles, whereas the Mariinsky production throws everything into the staging. The set, for all its minimalism, actually makes a powerful impression: Dodon's luxurious bed sits on bare earth, with coal strewn around, as if the action takes place at a mine. The aristocratic characters are given white costumes, but the lower parts are blackened, as if by the pervasive coal dust. The lowly characters are dressed fully in black. The suggestion appears to be that the country is rich in raw materials, and reliant on these, a situation that typically leads to acute social polarization. In Act III, the same shiny bed is set on caterpillar tracks as the sleepy Tsar returns from war – an image very much in the spirit of Rimsky-Korsakov's satire.

Another telling image appears in the design of the Queen of Shemakha's ‘tent’, which looks like a toppled and partly disassembled Tatlin's Tower, symbolizing a utopia gone wrong. The Queen herself, in Pelly's production, is an alluring sci-fi princess presiding over a tribe of amazons. She wears a body-hugging dress in the obligatory sci-fi silver, once glamorous, perhaps, but now moth-eaten, telling us all we need to know about the state of her realm. In the absence of any Matison-type distractions, the longueurs in her seduction scene make themselves evident, despite the top-notch singing and acting (Venera Gimadieva and Pavlo Hunka).

The Mariinsky's Queen of Shemakha is very different: she is Dodon's erotic dream come true, with floor-length blonde hair and a barely-there red dress, and the singer, Aida Garifullina, undoubtedly has the looks to support this presentation of her character. The sexualization of the Queen results in a more two-dimensional character than in Pelly's version, but even so, Garifullina's miraculous singing makes her the greatest attraction in the production. Gimadieva has a heavier timbre that complements the more rounded characterization, but she matches Garifullina's virtuosity every step of the way. Both sopranos happen to be from Kazan, Tatarstan, and one might jump to the conclusion that their casting as an oriental queen is ethnic typecasting. But this is not borne out by either of the productions, since Mattison and Pelly show no interest at all in indulging the opera's oriental stereotypes. Without the traditional oriental visuals, we can easily forget that the Queen's erotically charged music contains some oriental tropes, and this is quite revealing, since it allows us to hear a hidden kinship with the music of Tannhäuser's Venusberg.

Act I has a scene where a maidservant teases Dodon until he reveals the erotic nature of the dream that had troubled him earlier. Rimsky-Korsakov's music for the dream anticipates the Queen of Shemakha's music when she appears in the flesh in Act II, and the seduction takes place for real (in the traditional staging). Both directors have noted this connection in the score, and they have both responded by presenting the Act II seduction as a continuation of Dodon's dream. Although Matison's Queen more obviously fits the continued-dream scenario, it is Pelly who goes so far as to present Dodon, now in Act III, waking up from the dream because of the din of the wedding procession, a great grotesque climax in the score. Horrified, the Tsar tries to shelter his ears from the music and his mind from reality.

Matison's concrete Russian setting, its clear political satire and colourful slapstick ensure that the audience enjoys the spectacle from moment to moment. Pelly's more universal interpretation is darker and on balance more powerful, despite the longueurs where Rimsky-Korsakov's score needs the help of more stage activity. Speaking in purely musical terms, the Mariinsky's only big attraction is Garifullina's Queen. The orchestra, under Valery Gergiev, gives an accurate rendering of the score, but with the exception of Garifullina the other singers often fall behind, and their melodic contours sometimes suffer from imprecision. The studio sound production seems over-elaborate, creating an artificial soundscape that bears little relation to the staging, with the result that the singers in the video seem disconnected from the soundtrack, giving the strange impression that they were miming (an effect I have noticed on other Mariinsky DVDs).

The Mariinsky's Dodon, Vladimir Feliauer, delivers the role well enough, but La Monnaie's Pavlo Hunka comes across as both the better singer and actor. He brings Dodon to life and makes him more sympathetic, which is a bonus in this rather dehumanized fairy-tale spectacle. The orchestra under Alain Altinoglu also sounds more lively, giving Dodon's fake folk music an appealing lilt and providing witty comic details, such as the cor anglais representing the parrot with delightfully bent notes. Perhaps the Mariinsky is now a little jaded, since Rimsky-Korsakov is a permanent fixture in their repertoire (allowing them to play all 15 of the composer's operas for the 2019 anniversary). At La Monnaie, by contrast, this opera was an unusual departure from repertoire favourites.

There is another aspect of the video that we could easily overlook, since it is to be perceived in the Mariinsky auditorium rather than the stage or orchestra pit. The audience, shown before the performance begins, includes a large number of children, who came to see the matinee in the comfortable modern opera house recently built next to the original Imperial Mariinsky. These smartphone-generation children can easily latch on to the image of the hipster Cockerel-girl with her Doc Martens, sandwiches and selfies. We cannot see their reactions during the performance, so we can only speculate. Perhaps they enjoyed the gigantic trinket-box in which Dodon's world is hidden? Or the slithering snake that is projected onto it? Or the slapstick of the silly hats and ridiculous fights? The production works well for both adults and children. What of the seduction scene? Even there, a closer look shows that the Queen of Shemakha's provocative costume actually reveals little, since it is an assemblage of red and flesh-coloured panels. Although this overstuffed production loses out artistically on several counts to La Monnaie's sleeker and bleaker staging, it seems well calibrated to build up a new generation of operagoers.

While critics (myself included) try to read productions closely and exhaustively, this hardly reflects the experience of normal audience members, who are bound to miss at least half the goings-on in opera, which is, after all, an immersive multimedia genre. The under-tens who came to see the Mariinsky Cockerel will be unaware of the political satire, and the subtle erotic games will be meaningless to them. What they will remember is the bright colours, the magical transformations and disappearances, the people singing in impossibly high voices, the dry-ice fog on stage and their ice-creams during the interval. They will hope for their own cockerel backpacks. And all this means that they are likely to ask for future visits to the opera. Whatever its shortcomings, this is the Mariinsky production's huge saving grace.