Can AC synchronous motors be controlled with VESC?
Both {BLDC, PSMS} have PM on rotor, but the difference is the distribution of stator windings.


BLDC's are cheaper, better slightly more transient torque, when you do not need any   precise position control unless you have a position encoder feedback then other specs determine which is better like EMI, THD, current crest factor, but generally any Sine wave drive gives better servo control for smooth torque, and position control such as using a low cost (&lt;0.3$/W) VFD with some kV/RPM and computer control.

There are MANY types of position feedback encoders with different cost and resolutions. Cheapest and least accurate are Hall Sensors but adequate for commutation in most cases.

Both can be 2 phase quadrature or 3 phase Y  ( or more phases ).  ( You are considering 3 phase.)

Both tend to be 82% of no load speed at max rated power and 66% of no-load speed at max torque.

BLDC tend to be DC power with DC to Neutral or full bridge  while PSMS are full bridge such as simple velocity+ acceleration controlled or AC input power.

Both use full-bridge PWM control. Feedback options include: current , and back EMF while BLDC tend to use HALL Sensors and PSMS tend to use more precise position feedback ( 3 types).  ( Although I once use a micro-sized brush motor with 1000:1 gear reduction to turn a sin-cos Bourns pot for PLL vector rotation of a TEK XY vector display of an eddy current signal with 100 ppm resolution on impedance in XY planes at 100k,200kHz in late '70's)
PSMS may offer active brake after coil power is off as a safety feature,  while BLDC needs more active coil power for static torque.

Both can use  6 step Scalar control (quasi-sine) or FOC linear Vector true sine.

Both can have a variety of sensor feedback or used in sensorless control, depending on position accuracy and torque-phase jitter of control needed.  

For high-performance Servo's with PSMS are best for resolution, the linearity of current and THD of power and thus lower eddy current losses.

Depending on cost, performance compromises, BLDC can be better such as using inexpensive ESC controllers.

It all depends on your error tolerance for every spec. {Position, velocity, acceleration, EMI, power distortion, dynamic control specs {step response, overshoot, load regulation)

Kollmorgenoffers best in class Servo solutions with at least 3 different servo feedback solutions, Sin/Cos resolver, RS485 digital incremental encoder with 20 bit resolution or  

BLDC


Trapezoidal back emf   
Square wave current   
Concentrating winding   


More efficient , less servo position accuracy, more harmonic distortion

PMSM


Sinusoidal back emf   
Sinusoidal current   
Distributed winding   


If I made any errors in generalizations ( please suggest corrections) TYVM.