Hiya June4ever
In my opinion I would say that there is no significant difference.
All I can say is that I would use "It's important for me...", when I want to:
1. make a stronger statement, i.e. I must/have to do it.
"It's important for me to learn English."
2. make a comparitive statement, i.e. have this rather than something else.
"My neighbour is an American and therefore it's important for me to learn English (rather than any other language)."
3. convey a feeling of immediacy
"It's important for me to learn English now, if I am to speak with my American neighbour."
4. give a list of criteria, i.e. I must have this, that and the other.
"It's important for me to have a phone that can take photographs and connect to the web."
If I replace the above 4 statements with the words "It's important to me...", it does not sound right. Maybe it is something to do with the repetitiveness of 'to' that I don't like, anyway, if I replace "It's important for me to..." with "It's important to me that I...." then it sounds better.
I hope this helps you. Perhaps there is someone out there can explain this better in terms of grammar.