Please note that I am posting this question because I'm still not sure if I understand the difference although I did a comprehensive study of a great number of answers to the "for versus to" questions.
This issue turns out to be much more complicated than I expected. I chose to pick this among many and different questions still to be made.
(A) It is important FOR me to speak proper English.
(B) It is important TO me to speak proper English.
(A) It is important FOR me to speak proper English.
Could this imply that he or she is an English learner and wants to improve his or her English very much, making it possible to rephrase it as "it is important that I speak proper English?"
(B) It is important TO me to speak proper English.
Could this imply that he or she, presumably a native English speaker, expects English to be spoken properly no matter who the speaker is, making it possible to rephrase it as "it is important to me that English be spoken properly" or "speaking proper English is important to me?"
My guess is that they wouldn't be interchangeable and could have different meanings as above. I would appreciate any advice, hopefully including any rule of thumb.