The real advantage of a BLDC motor is the coils are switched in sequence with the rotor position, resulting in a high efficiency conversion of energy. This is similar to what brush DC motors do, only rather than "switches" being on the rotor that wear out, they are realized using solid state switches that don't (field effect transistors, or FETs). An advantage is speed can be directly controlled by altering the switching rate, where a brush DC motor you cannot do this.
Operations like running a compressor which sits at the same RPM for days on end would not take advantage of a BLDC motor. A simple synchronous AC motor is fine since they are made to be efficient with a 60hz sinusoid waveform. You are simply replacing the BLDC controller with an AC inverter. Pretty much the same thing at the end of the day only at a fixed RPM.
Where a BLDC motor may have an advantage is at initial startup. You could ramp the motor speed up gradually, resulting in a smaller current hit which could mean an easier to realize solar system.