Not all progestins are created equal. See the table on the pharmacodynamics of progestogens for on- and off-target effects.
CPA is used because it has absolutely excellent antiandrogenic (AA) effects (that ++ in the AA column). It does has glucocorticoidal effects but I suppose it's a compromise with being an excellent AA.
MPA I wouldn't recommend, it has androgenic effects and glucocorticoidal effects, both not good. Glucucorticoidal effects are especially worrisome long-term has they carry all kinds of nasty systemic side-effects.
Three progestins of note are
Drospirenone, both AA and and antimineralocorticoidal (AM) effects.
Dienogest, moderate AA effects and little else
Nomegestrol acetate, moderate AA effects
The problem will be to find those as standalone medicine. I don't even think they exist in this form. They are almost always combined with ethinylestradiol(bad) or estradiol/estradiol acetate (ok). They are certainly not as good AAs as CPA.
I mostly reiterate the same comments I made a while ago in this thread.