Dear Katz,
As you stated, both are correct. As for which is more widespread or popular, here is my perspective from observation of American English for the last decades:
"Appendixes" used to be absolutely incorrect. I would always correct "appendixes" to "appendices." Then, it seems that so many people made the error, that it started to become acceptable to the general public. I noticed it started to appear in academic and other published works. Both are now listed as correct in modern dictionaries.
I tend to think/feel that "appendices" is "more correct," but I think that's because I'm older and that's the way I was taught in high school. However, English is an ever-changing language and it seems to me that "appendixes" is becoming more popular.
When I have to choose one in my writing or in editing, I usually review other similar publications and try to be consistent with their choices.
Best,
Debra