In Classical Greek, is there a functional difference between the suffixes -esis and -osis?

Same gender (feminine), same function (forming abstract nouns); and in fact, same suffix, –sis. The –ē– and –ō– comes from the verb stem, not the suffix.

So phy-ō “grow” > phy-sis “nature”. kine-ō “move” > kinē-sis “movement”. psycho-ō “to animate” > psychō-sis.