Does the draft horse offer significant advantages over oxen when it comes to farming?
Aha! My area of expertise.
Draught horses were not commonly used for farming in Europe until the 1800s. Oxen were. Two oxen had roughly the same amount of power as a single horse, they were cheaper and easier to feed, and once they had grown too old to use, they could be eaten, where-as English people have long be unsure about eating horses.
It was in 1801 that the Enclosures Act came into place, which had the effect of making fields smaller. A traditional team of six or eight oxen was unwieldy and difficult to use in a small field, and a two horses could do just the same amount of work, and often quicker, if less steadily.
The main reason it seems that Europe used horses instead of oxen is because the rise of the draught horse and the invention of the camera pretty much coincided, so many of the old farming photographs show a fine pair of draught horses instead of the earlier oxen.
May I add a follow up question? Mules were commonly used in the United States, many descended from a donkey given to George Washington by the King of Spain. Washington is credited as an early proponent of the mule as a draft animal. Why were mules more commonly used in the US than in the Old World?
Is this true for all Europe, though? Because it is my understanding that oxen, not horses, where used in farming in Portugal, well into the 20th century.