Question

How do you know when to use the washer formula compared to using the cylinderical shells formula? or does it not matter

Answer 1

Whenever it's easier.

Answer 2

you sure?

Answer 3

That's how I make the decision. As you're trying to define your differential area, you'll see which way makes for a less nasty function to integrate.
I can't say for sure right now that both methods will work in all cases (they likely won't).