I have shot both. The 3/8" is lighter and tends to have more variation in shape. It is expected as it is much cheaper per ball. They tends to be more sensitive to cross wind, so shooting indoor gets better results. I don't get to shoot indoor so I need to more conscious of the wind, which is a training in itself.
The 1/2" is more consistent in shape for more than double the price per ball. It is better ballistically, so it is doing better outdoor. I believe it also has higher "muzzle energy". The ball is bigger. It may feel funny with a small pouch.
I like the 1/2", but I will still buy 3/8" for it's low price. I will try out the 3/8" steel balls. If it works out, I actually may stop buying the 1/2" clay, and stay with 3/8" clay and steel.
-TL
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