The quarter test on euphonium mouthpieces is really a test of cup width, not depth so much. With our common sizes, the quarter hits the side long before it would hit the bottom.
As far as inner rim sharpness, there are a lot of factors that affect how the rim feels, and the apparent sharpness of a particular rim may be caused by other things. Check out this page:
http://www.grmouthpieces.com/rim.html
In his lexicon you are talking about the "bite" of the mouthpiece.