Do you think Westrosi knights are as good at horsemanship and mounted combat as Dothraki? Knights spend a great deal of time practicing the art; they even travel the kingdom going to tournaments to display this skill. Does that put them close?

As good is hard to say. They learn a completely different kind of mounted combat from the Dothraki and depending on a number of factors (terrain, coordination with infantry, skill of leadership, etc.) it might match up horribly or well with the Dothraki model. 

To use some real world examples: the Mongols beat the shit out of European knights when they first came in contact with them. The Mongols also beat the living hell out of the Arabs and the Turks who often used the same kind of feigned retreat, highly mobile, all-cavalry, horse-archer-based tactics that the Mongols did. Is the reason that the Mongols beat the Europeans is that horse archers are better than knights full-stop, or because Genghis Khan’s armies were some of the best-trained and best-led soldiers in world history?

To further extend my argument: Hulagu Khan, grandson of Genghis, who had sacked Baghdad and brought the Abbasid Caliphate to an end, two years later got completely demolished by the Mamluks of Egypt at Ain Jalut and the First Battle of the Horns. Sixty years after the first and successful Mongol invasion of Europe, the Mongols invaded Poland and Hungary again and were beaten badly. 

So is that technology or the other myriad factors (leadership, numbers, terrain, logistics, weather, pure blind luck) that can determine victory or defeat? I lean to the latter.