Horses are judged against breed standards and ideals for specific disciplines. For instance, if you are showing in halter at an open show, the horses should be judged and placed according to how well they meet their specific breed ideals. The same goes for western pleasure, hunter under saddle, hunter over fences, etc., where the horse is evaluated based on their similarity to the ideal movement for that breed. In an open show situation when mixed breeds are exhibited in the same class, the horse that most closely represents their breed for that class will be rewarded with most positive placings.
Showmanship, horsemanship, and equitation classes are scored and placed based on how accurately and efficiently the handler/rider performs a pattern. Other classes, such as trail, western riding, reining, etc. are actually scored, so there are very objective standards as to how the horses should be placed in the classes.
It's not possible to speak to your specific experience at an open show, but the horse that best meets the standards and ideals for that class should come out on top, no matter what the breed. And remember, a big part of showing horses is acknowledging that the score is one person's opinion on that day, in that class.
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