I’ve seen a number of different sources claiming that you should use a stainless steel screwdriver or bit insert to drive stainless steel screws, but Wera does the best job of explaining why:
Stainless steel does not rust. However, if conventional steel tools are used on stainless steel elements or stainless steel screws the wear debris of these tools can adhere to the surface an begin to rust. This effect, known as extraneous rust, can impair the visual impact and even cause structural damage, resulting in high costs for the necessary repair work.
This sounds all well and good, but stainless steel screwdrivers aren’t as hard as screwdrivers made from other materials, so Wera solves this with their new vacuum ice hardening process. If I understand the process correctly, they allow the steel to cool in a cryogenic vacuum chamber.
Wera uses their multi-material Kraftform handles on all their stainless steel screwdrivers. They designed the handles to fit the shape of your hand and not roll away when you put them down. Many of these stainless steel screwdrivers also feature their Lasertip etching, which grips the screw head when engaged.
You can buy the stainless steel screwdrivers in a variety of types and sizes — for example, a set with 2 Phillips head and 4 slotted head screwdrivers plus holding rack starts around $40 before shipping.