If you had 2 identical props, one in aluminum and one in stainless, the stainless prop would give you a little better performance.
This is because the stainless prop will flex less under a load.
However... it isn't quite that simple because you will never find those 2 identical props in SS and AL.
The biggest difference between the two materials has to do with the area where you operate. If you routinely operate in shallow water where rocks or other subsurface obstructions might be present, an aluminum prop is preferred.
Reason being that an aluminum prop will 'give' a bit when struck, and not transmit all of the force to your lower units gear case. A stainless prop has almost no 'give', and will transmit most of the shock directly to your lower unit.
The area where I work has a lot of shallow water, and hidden (subsurface) rock groins that have taken many props (and at least one entire lower unit) from our rescue boats. We would never even think of putting a stainless prop on any of these boats (21 SE's).
The area where I live does have some shallow areas (~5'), but for the most part the bottom is soft. The majority of the area around where I live is 25' to 125', so I have a stainless prop on my boat.
So... it's not just about performance. If your waters are deep and the subsurface hazards minimal, a stainless prop will generally give better performance.
If your waters are shallow with subsurface obstructions, stick with aluminum for a little more protection for your lower unit.