I wonder whether these two phrases are different in their usages.
In my understanding, 'speak well of' can be used only when talking about somebody, as in 'He was speaking well of you." In contrast, 'say good things about' can be used when talking about both somebody and something, as in 'He was saying good things about her paintings.'
I would be more concerned with the fact that the first is a more formal, fixed phrase.
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I would be more concerned with the fact that the first is a more formal, fixed phrase.