I think I'd use them slightly differently:
It's interesting for me to hear that - an interesting experience for me.
It's interesting to me to hear that - I find the information interesting.
That grammar rule is new for me - I've come across a lot of grammar rules but this one is a new experience for me.
That grammar rule is new to me - I've never come across it before.
The first pair (interesting for/to) seem to me to be a much more genuine choice between different meanings.
The second pair (new for/to) are really very similar and to would be much more natural to or for me than would for.