There are no easy, concise, answers and one technology is not necessarily better than the other. Once you have completed your homework, the decision for an AC or DC motor system is dependent on application and cost. In the end, markets exist for both AC and DC, and there are clearly advantages and disadvantages to both.
DC motors have the advantage of: higher starting torque, quick starting and stopping, reversing, variable speeds with voltage input and they are easier and cheaper to control than AC.
AC motor advantages include: lower power demand on start and minimal maintenance. While the market for AC motors is larger than DC, it can be challenging to find AC solutions with fractional horsepower ratings.
Demand is growing for 12 and 24V motors to support solar, marine and portable (truck mounted) equipment which DC technology readily supports. DC technology is more cost effective than AC in general for lower horsepower applications. DC motors are the older of the two technologies, but R&D has not ended. Motor companies continue to invest in technology to reduce maintenance costs and extend motor life.