Well alot of the differences are all about temperature and having the appropriate materials to survive in the enviroment.
There are differences in the wheel designs too though.
The requirements for a diesel and a petrol turbo differ in that in a diesel you have a shorter range needed as the gas flows are more limited. As a diesel only revs to in the region of 4000RPM for most passenger cars this can flow at lot less then the equivalent sized petrol engine with a speed around 7000RPM and the wheels have to be designed for the required range.
This difference is seen more on compressor wheel design then the turbine stage as we would tend to have a wastegate (or VNT - variable nozzle turbine) to control the flow through the turbine stage so we can match the range of the wheel to the engine operation we desire and then wastegate off the excess flow at higher engine speeds).
With regards to a tuned diesel... a material more often seen on petrol may offer benefits, it depends on how they have tuned the engine.
You could just increase boost. air fuel ratio will be the same (same lambda or excess air) so the exhaust temperatures should stay within limits for a diesel style turbo (however the increase in in-cylinder pressure, air temperature in the manifold, turbo-speed could cause durability problems).
If you lower the excess air or AFR you will generate more in-cylinder pressure. here the temperatures may lead you to selecting a more durable material as used in petrol applications, however the negatives from going this route are greater then increasing boost pressure... so this route is unlikely...
Although saying all that we dont specifically have materials we match to petrol or diesel, we use the appropriate material for the application... we have a range of different materials / technology that we will apply when the application demands it, be it petrol, diesel, passenger car, truck or whatever....