Which winding is the auxillary winding in a permanent split capacitor motor?
I have started to doubt my thought that the lower resistance winding would be the one with the additional capacitive impedance in series. I have seen a couple of trouble-shooting guides that say the opposite. However the guides I saw seemed to refer to specific purpose motors, heating and A/C fan motors, I think. Appliance and equipment motors have undergone many years of optimization to produce motors that are exactly suited to the load with minimum cost. All dishwasher motors are likely to be similar, but not necessarily the same as furnace blower motors.

I know that there are PSC motors that are designed with two identical windings to make it simple to reverse the direction of rotation. That is obviously not the case here, but that illustrates the extent of variability PSC motor designs.

The best way to determine the connection remains identification by examination of the original wiring. Another reasonable alternative would be to examine or find documentation for a similar appliance.

Because of the water heater in most dishwashers, it is difficult to determine from sales literature how much current the pump motor draws. If it is as little as 2 amps, the lost heat in the 16 ohm winding would be 48 watts. That seems like a lot for a motor that might require only 400 watts in normal operation, but motors of that size and type may have only 50% or 60% efficiency. If the motor takes 5 amps and most of it goes through the 16 ohm winding, that would mean 400 watts dissipated in the winding. That would burn it up pretty fast. On the other hand, if the 4 ohm winding is assumed to be the main winding and the self inductance is not as high as it would be for a main winding, the current could be too high.

If you want to proceed on the basis of someone's guest guess, have an ammeter in place during the test. Clamp-on ammeters are available at a reasonable price and very good to have for anyone who does electrical DIY projects etc. It will be easier to instantly see a problem with an analog meter. However you do need to be aware that for the first fraction of a second, the current will normally be quite high. Connect the motor through a switch that is easy to operate and close to the ammeter. Switch off immediately if either the ammeter or the sound of the motor is not what you expect.

If you can, look at the size of the wire used for the motor windings. If some windings use larger windings, you can be sure those are part of the main winding. That also indicates the relative current in each winding.

If you determine which connection seems to be better, check the temperature of the motor carefully during initial operation. Disconnect if it seems to be heating up to much or too quickly. Measure the current in each winding. It is possible the either connection may appear to work. Either connection may be viable with no-load operation. If that is the case, you won't know if you have the correct connection until you put a load on the motor.