4 Ohm vs 8 Ohm Crossover

I've always wondered given two of the same driver, one being 4 Ohm and the other 8 ohm, what would be the specific differences in the crossover design and components between the two?

Do the same differences apply whether it be a tweeter or woofer?

For a 4 ohm driver (compared to a crossover for an 8 ohm driver as reference):

-Inductor coils will need to be HALF the original inductance value
-Resistors will need to be HALF the original resistance value
-Capacitors will need to be TWICE the original capacitance value

... to achieve the same response, as the same-design crossover made to use with an 8 ohm speaker.

Yes, it will apply no matter what the driver, whether it be woofer, mid or tweeter. And will apply no matter where the components are used within the crossover network...

Regards,
Gordon.

Thanks for the very clear and straight forward rundown.

BTW what issues would crop up by replacing either woofer or tweeter into the opposing 4 or 8 ohm crossover? Anything potentially catastrophic?

If the driver's impedance doesn't match the crossover, you'll either see a suckout or a hole in the response due to the crossing point being too high, or risk damage to the driver (tweeter's especially) from the crossing frequency being too low.
In other word's, the overall frequency response of the speaker will change for the worse.