To me "class" encompasses all the more difficult to measure aspects of thoroughbred ability like stamina, acceleration, gate speed, versatility, heart, determination etc.... As you move up the class ladder, horses tend to earn faster speed figures, but they also tend to run faster paces and have more of the qualities from above.

IMO, most horses earn their best figures when they run against other horses of similar or weaker quality because the pace, race development, and demands of the races tend to be easier for them. There are exceptions, but IMO typically when horses make sharp moves up and down the class ladder it matters (especially if they tend to get involved on or close to the pace).