An induction motor is definately cheaper to build....more reliable....or at least less looking after...
As for efficiency, a brush type motor could have better torque at startup...and be made to speed control more readily.
Jeff
There is a growing list of large companies that will not allow a machine with a brush motor inside their plant for good reason. If you have a plant with a thousand brush motors you will have 3 or 4 brush related problems per day. With the current maintenace tracking software employed by the automotive industry anything that breaks down that much will be replaced if possible.
This rule holds true for any component that has a wear item, like the old bronze worm gears.
This being said, if you need a really cheap speed control with a great speed range you can not beat a brush DC motor and control. If this is for home use or a non-critical application DC brush is the right answer. The cost of AC VFD's are coming down every year and their performance is going up but they have not yet reached the cost effectiveness of a DC brush.
In a brush motor (DC), you have the field poles mounted on the frame and a wound armature whereas a brushless motor (DC) has a permanent magnet rotor and a wound stator. A brushless motor has no brushes to wear and replace and because of the lack of brushes, you can expect to have lower frictional and electrical losses. Also, there is no commutator to wear. Brushless motors offer improved heat dissipation over brush motors since the winding is located on the frame. This creates an additional benefit, that is, the permanent magnet rotor in general is lighter than a wound armature for the same HP rating resulting in less inertia. Brushless motors can deliver a higher peak power output since they are not mechanically limited by the brushes and commutator that, under severe conditions, can create sparking. To sum it up, a brushless design will give you less maintenance and better efficiency but a brush motor often is somewhat cheaper. Also, brushless motors require a drive amplifier to vary winding current based on rotor position feedback.
I assume you refer to "DC Brushless Motors".
If that is your question, eemotor (Electrical) gave a good resume of permanent magnet version (edge technology). I wonder if permanent magnets are available and cost effective for Hugh industrial size applications.
Coupled to a proper Variable Frequency Drive an SCIM (shorted circuit induction motor or better known as squirrel cage motor) is able to duplicate most of the traditional commutator DC Motor performance, but is not a 100% equivalent.
The benefits of getting rid of brushes are evident.