The dictionary ascribes the same purpose to both these suffixes: to denote 'to make, or become'.
However, for some neologisms, -ize seems much more appropriate than -ify does, and vice-versa.
There must be some reason for this.
Is there a rule that governs, or describes, when to use one over the other?
Best Answer
Courtesy of @DanBron, here's what it says in Word Formation in English,
with interpolated translations:
Translation: there are restrictions on what kind of words -ify can go on. They have to sound right. Examples of each kind of word root with -ify:
Translation: the set of roots that can take -ify and the set of roots that can take -ize are (almost) disjoint sets. There is one intersection, which will be described next.
Translation: you can do it either way with words stressed on the next-to-last syllable that end in unstressed /i/. But they're the only ones.
Translation: -ify and -ize can be considered "the same morpheme", just like a and an.
Translation: there are a lot of kinds of meaning (poly-semous < Gk 'many meanings') for the suffix. These types have technical names. Examples follow (I've changed a few old-fashioned terms to protect the innocent).
Translation: A lot of funny things happen to the roots when adding -ize. Examples follow.
Translation: most of the non-neologisms were formed in Latin, under Latin phonological and morphological rules, which don't apply to English. So lots of the roots are not really English words, but rather are related to English words, and it gets very complicated trying to account for all the differences between the roots and the words.
This is one example of how complex even a teensy-weensy part of English grammar can get.
And this isn't even syntax.