What makes a great work of art? There are many answers to that question, but mine is simple: “depth”. There must be many meanings, many emotions, many possible reactions contained within it, and each time you look at it, you should be able to find something new. On that count, if you compare the two great women’s portraits of today’s Paris, the Mona Lisa (La Joconde) and the “Lady and the Unicorn” (La Dame à la licorne) tapestries, there’s no doubt in my mind which comes out as the greater piece of art.

Leonardo De Vinci’s is a fine piece of workmanship, and its artistic framework is closer to that of our own time and traditional ideas of “beautiful art” (as attested by 1,000s of placemats and cheap prints it has spawned all around the world). But see it once, contemplate the really-not-so-mysterious smile, and you feel that you’ve looked at an icon, not a work of art that will repay multiple visits and further study, unless you’re very into arcane details of Renaissance symbolism.The 19th-century Symbolists might have found in this image of Lisa del Giocondo their ideal of “perfect womanhood”, but it is a rather empty, shallow ideal – fitting perhaps that in common parlance she has lost her own name and become a mere symbol.

“The Lady and the Unicorn”, but contrast, is in its medieval sensibilities, far more foreign to our eye, far less immediately accesible, but visit it, and visit again, and you’ll find depths, feelings for everyone and every time. On my latest visit, in the great dark vault at the Cluny Museum (Musée du Moyen-Age) it was the, of the six tapestries depicting different senses, “Touch” that spoke to me most – I saw in it a woman facing a great and difficult choice, a challenge, a Joan of Arc who foresees a tragic end to the path she’s taking but has decided to follow that destiny anyway.

Yet my diary from a visit two decades ago tells me that then I was held rapt by “Sight”, where the lady holds a mirror up in which the unicorn admires his own super-cute reflection, but she looks on sadly, reflectively. She was musing, I felt sure on the the fragility and shortness of beauty, of life itself. Of course in both of those cases my feelings reflected events in my own life, but there was contained within the tapestries – these works of some great unknown Flemish workshop of the late 15th century.

But it seems from the crowds in the museum that everyone gets something from the tapestries – even the children, enraptured by the delightfully rendered domestic animals that are packed into the fields of flowers.

That we know so little about the tapestries has of course bred a whole academic industry to rival Mona’s – indeed there are many more mysteries here. Most academic opinion has settled on the commissioning family as the Le Listes, a bourgeois family from Lyon that moved in Bourbon court circles. Quite a bit is known about the men of the family but, typically for the period, almost nothing of the women. But it seems anyway that this is not one particular woman, but an allegory of femaleness and myth. But in the details lie the controversy.

If you haven’t read it before seeing the tapestires, I’d recommend holding off reading Tracey Chevalier’s fine historical romance, titled simply The Lady and the Unicorn. It is a fine work of popular history, but while the research is solid this is a fiction – not the real story of the tapestries. But it is a reminder that while the artist who draw these images was certainly male, and the primary weavers probably were too, there are within these threads much women’s labour, much women’s struggle, and somehow that seems to speak through the wool.

So there is, at the heart of these tapestries an emptiness, but it is an emptiness of possibility, of multiple meanings and complexity, that the small mysteries of the Mona Lisa can’t hope to match.