Brushed motors tend to have better low speed resolution, better drag brake, and are typically cheaper to produce. They will function under water (at the cost of reduced lifespan).
But, they can be maintenance intensive if you want speed, and they will eventually wear out.
Brushless motors require very little maintenance, are capable of producing stupid speed and power, but many don't have very good low end control, and they tend to be more expensive. The sensored versions that are desirable for crawling don't like water.