Considering Wellesley's official attitude in India, respecting local law and custom to an extent that infuriated most of his own subordinates- and for that reason did not long outlast him, unfortunately- he would have been the ideal man to send into such a culturally divergent situation; oh, his private opinions would probably have been at least as caustic as Tarleton's, but he would have done a much better job of keeping them to himself, and keeping on terms with the Spanish.
What Tarleton was was a cavalryman; he believed in movement, in running, manoeuvring war, in raid and ambush- but he did not have the sense of the possible to let him know what was and was not a feasible movement. No grasp of logistics, artillery or engineering at all, and not the patience to listen to his specialists- Wellesley ran his army in supremely autocratic style, which did not sit well with the Canadians at all until they realized they were winning, but he listened and let men like Dickson advocate, at least.
Worth noting that Davout and Wellesley had a lot in common as generals; considering that Davout had no liking at all for the Spanish, nor they for him- he was worse than Protestant in Spanish eyes, being an ex-Catholic- it is astonishing he managed to get as much service out of them as he did. They respected him, but they never liked him. Wellesley would probably have had similar results, if character has anything to do with it.
The hinge of history here is Davout's presence or absence from the Grande Armee, I reckon; he should have been recalled, instead of wasting his time in a largely pacified province of the Empire- even at that, he came within what, two hours of saving the empire, tearing the Coalition's southern flank, the Austrian- Russian armies, to shreds, with Spanish troops playing a large part in that, but Napoleon never got the word in time.