Motor guy here, not into quad copters though. Brushless motors with optimally tuned software can have higher efficiency which translates to longer battery life. The downside is you need 3 half-bridges to drive one. A brush motor spinning in one direction needs only a single low-side FET. The cost in transistors and software is significantly higher for brushless, but the efficiency gain is real. I'm not so sure about any dynamic performance benefit, you can do about the same with a brushed motor if you're willing to drive it with a full H-bridge.