I wanted the rudder parts to be 1½" thick, and thought I'd make it out of two layers of ¾". Then I thought there might be an advantage in making it out of four layers of ⅜". I chose exterior fir ply because the whole boat is that, so no point in adding fancy.
One reason to go with the ⅜" ply was the number of plies per sheet. At the lumber yard I looked at both ¾" and ⅜". The ¾" had six plies. The ⅜" had four. So 1½" of ¾" ply would have 12 plies, whereas the equivalent thickness in ⅜" (four layers) has 16, a third more.
Another factor that decided me on the ⅜" was that the pintles from the old rudder are for ¾" stock. If I wanted to use them and also have the rudder stock be 1½" thick, I'd have to install them on a core ¾" thick, and put a ⅜" cheek on each side. I needed either a half sheet of ¾" or a full sheet of ⅜". Simpler to go with the ⅜", even though it meant more cutting and gluing. And stronger, because of the additional plies. I had it cut in half at the yard so that I could manage it, another reason to go with the thinner wood.
Here's a picture of my bathroom floor. I chose it to glue on because I wanted to make sure the core layers were straight and flat, and I'm pretty sure my bathroom floor is good. The orange/red circle shows where the top of the blade is on the other side of the stock, and also shows the minimum contact area of the two pieces. It's a 12" diameter circle. I was working out how tall the whole rudder will be (53"). It will extend 12" below the skeg on the Firefly.