I cannot easily figure out which one is more appropriate to use:
It's important to me.
It's important for me.
Are they the same? If not, what's the difference?
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The simple explanation is that "important to" is something you value, while "important for" is something you need, or that will help you in some way.
A nice example is:
"It is important for you to get well" ~ your life will be improved by returning to health
"It is important to your family that you get well" ~ they put a high value on you being healthy.
There is a large grey area, particularly if you are talking about personal experiences. Passing an exam, for example, is something you put a high value on (or you would never have started the course) and will also benefit you in terms of career. In this case, it is 'important to' and 'important for' you.
The word for is used to address the object, target or use of an action/activity. It's also used for rightness.
'Important for' me - in my opinion, this is essential.
Getting this job is very important for me, I'm in great financial crises.
On the other hand,
'Important to' is to show the direction toward - I'm the receiver, it'll affect me.
My kid's education is very important to me, I'll put her in the best school in the town.
In most cases the to part would work for the for one but not the other way around. In your example, they probably means the same thing. But if you are picky, the first one means that whatever you are talking about is important to you because it's affecting you. In the second one you are merely expressing your thoughts and the thing may or may not affect you.