Servomotor is a type of motor with position control. It’s unclear to me if that leadshine is an AC motor(leadshine site says yes)or DC, while ClearPaths are DC motors. Both types are brushless. The difference is in the type of voltage they use and control electronics.
In principle all servo motors operate the same, a motor(AC, DC, stepper, linear etc.), and encoder(many types exist, doesn’t matter here) that records the position and a drive with the electronics and logic to run the control loop. Mostly this is done by a separate drive but in ClearPaths case all this is built into the motor itself. All you need is power.
As far a pros and cons are, to me they seem to be:
Easy to hack
Motors are off the shelf and cheap, as are encoders.
Hobby product, no professional support.
No finished software, lacks polishing and features.
No industrial standard controls.
necessary to tinker and understand the basics of electronics and motors to use.(you can fry the board)
Not reliable enough(in the industrial sense).
Various sizes and power available.
Good management software.
Autotuning and other useful features.
Compact and safe design.
Easy to handle and use.
Expensive(more than Chinese AC servos, for equivalent you have to spend 500 per motor, 250 per power supply and maybe some other bits as well, close to 1k per axis.)
Lack of many industrial controls(no ethercat, canopen or any other industrial standards, just step/dir and analog with an extra piece of hardware)
Just because they seem to do the same thing, doesn’t really mean they should be compared to each other.