"Close" butters no parsnips in war. And Bessieres' insubordination consisted mainly of refusing an order to attack the formed squares of the Light Division with the cavalry of the Imperial Guard - an order he was entirely right to refuse, as it would only have got the Guard slaughtered for no conceivable advantage. Oh, he also refused to fetch ammunition from Ciudad Rodrigo when the French batteries were running low, but the battle was effectively over by that point with the French having failed to secure any of their objectives.
Bluntly, Wellington beat every French general who came against him, up to and including Napoleon himself. Some, like Massena, had their careers ruined as a consequence. One of the reasons why Davout's reputation stands so high by contrast is that it never got tainted by an encounter with Wellington. If he had have gone to the Peninsula he would have had no more luck than any of the others.
Okay, hear me out-I don't deny that ordering the Imperial Guard cavalry to charge the British squares would have been suicidal. But, the cavalry could have been used to defeat its British counterpart, which it greatly outnumbered. We know that during the battle, when the French brought forward cavalry, 7th division formed square. When they deployed cannons, the English cavalry would charge. But, if the British horse had been neutralized, there would have been nothing to stop the French artillery from blasting the squares to pieces.
Besides the fact that Bessiere's judgment call was highly questionable, would the destruction of a division have been enough to compel Wellington to retreat? I don't know. But I don't think we should rule it out.
To adress a wider question, would Davout have been beaten if he had been sent to Spain? Almost certainly. The combination of Wellington's skill, the guerillas, and high command rivalry would have been too much for any of Napoleon's marshals to handle. But outside of Spain (maybe Quatres Bras?) Davout's chances in a confrontation would be good.