The primary type of single-phase motor used in refrigeration is PSC—permanent split-capacitor type. Study case 4 at URL
www.lmphotonics.com/single_phase_m.htm The compressor locked-rotor current will be on an equipment nameplate, to give an idea what sort of load it presents when started. With the unswitched run capacitor, shaft torque is dynamic in that phase shift [voltage angle] between the run and auxiliary windings is low at the initial zero-speed condition. A start capacitor increases the voltage angle for a moment until the kit’s relay senses high-enough voltage across the auxiliary wining.
One relationship of start-to-run currents can be understood by comparing compressor steady-state running impedance in ohms at full-load current to the DC resistance (in ohms) of the main stator winding. The kit may not reduce starting-voltage drop so much as reduce the time it exists. [No free lunch.] Understand also that there are two types of start kits. Most common it the all-in-one type that is more of a “fits-all” variety, versus a discrete electrolytic {starting} capacitor and separate potential relay that is specified by the compressor OEM. A third type is the two-lead PTC resistor, but has limited effectiveness and popularity.
In hermetic compressors, a popular mechanical style gaining ground is the “scroll” compressor versus older reciprocating type, that takes less effort to start. An unavoidable problem is that sometimes humans are sensitive to changes in voltage to varying degrees with incandescent lighting, so it bothers some folks more than others. On a 120-volt base, a standard minimum is 110 volts, but in some cases, 106 volts.
Let the guy install the hard-start kit if he will guarantee results to your satisfaction. Be well aware that if the start kit’s relay contacts stick or weld, your compressor stator will be cooked in short order.