A brushed motor uses a mechanical solution to move the magnetic field and cause rotation. A brushless motor uses electronics to achieve the same.
Compared to a brushless motor a brushed motor will be less expensive, be less efficient (a consideration for battery driven tools), make more noise, and the brushes will wear down over time.
In practical terms for something used occasionally both will be fine. Brushes take a long time to wear down and there is often replacement brushes included. Personally I have noticed that some of my brushed tools will throw sparks at times - if you're working around flamable stuff or gases that might be worth a thought too.