Why is Cheby 2 filter uncommon?
Have a look at this plot from this page at the Mathworks site:



The main issue is, as that page says:


  The frequency input to the Chebyshev Type II design function sets the beginning of the stopband rather than the end of the passband.


As you can see, the Chebyshev Type I filter has controllable passband gain out to the cutoff frequency.  That is not true for the Type II: Only the stopband gain is controllable there.  The passband roll-off for Type II makes it not very interesting for most purposes.