All motors are close to a dead short when power is first applied (locked rotor curent), the only resistance is the wire in the windings. The start windings have smaller wire so they have more resistance than the run windings. The difference in the resistance splits the phase causing a rotating magnetic field that pulls on the rotor, when a run cap is in the start circuit it splits the phase even further increasing the torque or the magnetic pull on the rotor. When a start cap is introduced into the start circuit it splits the phase even more but it can only be in the circuit for a split second because it can't take the current like a run cap. After the motor starts the rotation of the motor induces what's called inductive reactance or induced resistance reducing the current draw to the rated running current.
When they design split phase motors they calculate just how much capacitance the run cap has to be and what size start cap should be used for optimal starting efficency along with how long the starting relay will hold the start cap in the circuit. If it drops out to fast it hurts the starting time and if it stays in to long the motor current goes up not down and will cause start cap failure. Supco can't make enough units to match all the different size compressor motors out there, they are one size fits all and aren't matched to your compressor windings like the factory caps and relays are. When I used to buy replacement compressors they would come with new run caps and start caps and relay for a reason, in many cases if it was a warranty compressor I would have to sent the old caps back with the compressor or no warranty.
Like I said I did it for a living and worked on 1000s of split phase compressors and if you don't use the right parts they don't work right but its your money so do whatever you want. But I think you better look at your generator not your ac unit.
Denny