AC motor VS DC motor for high starting torque

Actually, AC motor can be also applied with the used of AC Drive, Frequency Inverter. However, based on my actual encountered of almost different type of motors, from fractional size to medium voltage size, from various Manufacturing Industries particularly in Cement Plant, you have to oversize the AC Motor to match the torque carried by the DC Motor.

However, AC motor with Vector variable frequency drive can give you around 200% torque at 0 RPM and very good speed regulation (closed Loop mode). They are now getting the AC packages close to DC performance is his respect. As you know, AC has some main benefits over DC.

The remarks above about DC and AC motors are correct, and ultimate choice depends on your requirements and external issues.
If your high torque fluctuates, i.e. you have requirements for short peaks (say a few seconds) then you can overload a shunt field DC motor in ways you cannot do with an AC Drive combination.
External ventilation is necessary in that situation, and be sure to specify it because of forces operating on the rotor and stator/pole windings.

DC motor does require more maintenance, and some more experience in installation and proper tuning (location of the brushes can be critical). The motor should be protected against loss of field, as that will cause excessive speed.

Like an AC motor a DC motor is suited for 4 quadrant use, provided that its grid can absorb and deliver the power.
What in some situations can be an advantage is that a DC motor only requires real power, conductor sizes do not have to take into account reactive currents or power factors. This however usually is not a deciding factor.