There is no single 'nuance'. Both prepositions have multiple uses (according to one dictionary, 'of' has 17 definitions and 'from' has 7, but that hardly suggests their range of use) and several of those overlap. I don't think nuances will help you, though, since your example sentences exhibit none, but take only one preposition each: I'm proud of you.
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ljswaveI'm nice to you.I do nice things for you. I do things that please you.