Why would I use a Nylon Millar Catheter over a Polyimide one, or vice-versa?

The only difference between the Polyimide and Nylon catheters is  a slight variance in the stiffness of the lumen. The Polyimide catheter material can feel slightly stiffer than it's Nylon counterpart.
Otherwise using one material over the other does not confer any advantages - it is purely a matter of preference.