Which one should be used?
To me, it makes no difference, but I'm not really sure why.
For me, it makes no difference, but I'm not really sure why.
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I think the general (most widely-applicable) one would be "to me". To my knowledge, it can be used in any of these cases where "for me" is used, and in some where "for me" can't be used.
For me, this is not a difficult problem.
To me, this is not a difficult problem.
Both of the above are fine.
But look at the following pair (the "*" sentence is ungrammatical in this context):
*For me, he is an idiot.
To me, he is an idiot.
The first example doesn't work as a way to express opinion, but "to me" still works fine.
Hmm, tough one. Rearranging the sentences helped me see this a little more clearly:
It makes no difference to me
This suggests there is no effect on me materially, emotionally, financially ...etc. That is, nothing will happen to me.
It makes no difference for me
This suggests that I have no strong opinion on this.
I can't explain this in terms of grammar or style, it's just a feeling that the sentences provoked when I said them to myself.
I basically agree with Antony Quinn's answer, with one slight difference. for me implies that your decision will not affect me. to me means I don't much care what you decide, even if it does affect me.
Illustration: My employer considers switching from issuing pay checks every week to issuing them once a quarter. This affects me, and I don't want it to happen, so I might say, It makes a difference for me (because my cash flow cannot handle this). (Sorry that I couldn't think of an example that kept the "no difference" idea.) However, if my employer considers switching from weekly to biweekly pay checks, it still affects me, but not in any way that matters to me (because my cash flow can handle this), so I might say, It makes no difference to me.