You cannot cast a stainless steel spool. Aluminum or Plastic is OK.
The narrower spool is easier to cast, because the line gets harder to pull off, as the diameter of the spool gets smaller. You might get a little more distance from a wide spool, but it isn't (IMO) worth it.
If you're fishing with braided line, there is no need for a wide spool. They date to the era of mono line. Narrower spools are preferable for braid, it's easier to thumb line back and forth, and there's less mass to control on the cast, whether you're using your thumb or relying on magnetic or centrifugal brakes.