Both paintings are oil on panel but the Louvre version has been transferred to canvass. The painting may have suffered some damage during the transfer process but it's condition is now stable.
The Leonardo exhibition at the National Gallery in London (Leonardo da Vinci, Painter at the Court of Milan) displayed these two works together in the same room for the first time ever. Although never achieving the same monumental impression gained by seeing the works in the flesh, I have placed images of the paintings side by side so that direct comparisons of the similarities and differences can be made.
The Virgin of the Rocks was commissioned (not long after Leonardo's move to Milan) by the Franciscan Confraternity in the Church of San Francesco Grande. Leonardo was assisted by two local artists, the Predis brothers, their task was to create an altarpiece for the recently completed chapel dedicated to the Immaculate Conception of the Virgin Mary. The Predis brothers completed two side panels while da Vinci painted the centre panel.
Shortly after the altarpiece was finished the artists became embroidered in a dispute about payment resulting in the artists threatening to sell the work to a rival bidder. It is likely that this dispute resulted in the making of the second version of the Virgin of the Rocks, the one now in the National Gallery in London, and in fact it was the London Virgin that was placed in the chapel in San Francesco Grande. The original Paris version was quickly sold to an art lover soon after completion.