In my head, “illusionary” describes stage magicians (illusionists) or their performances. I don’t really expect anyone else to use the same definition, but that’s always the first thing I think of.
Illusory is just anything that’s an illusion, deceptive or imagined.
For the specific context of ineffective approaches to global warming, I wonder if a term like delusional might be better, since it is characterized by “false or unrealistic beliefs” or “belief held with strong conviction despite evidence to the contrary.”