Aren't these tags synonyms? If they are synonyms, which tag should we use?
I agree that they are synonymous in practice. I suggest using only pronunciation, not only because it is already more common, but also because it is the less technical term, and thus probably more widely understood.
I think there's a distinction, but the tag wikis should make it clear (as seen in some other SO communities: "Don't use this tag for:"). Phonology is a science that uses special terms for sounds. A phonological answer would be of a little value to someone asking a question on pronunciation because they might not understand the terms or their symbols. A non-phonological answer might be usable, but presumably of very low quality, to a phonological question.
Situations I have in mind:
Is the open-mid front unrounded vowel an acceptable allophone for Esperanto's e? phonology
I agree with Marcos Cramer on using pronunciation primarily, but not because they'd be synonymous, rather than because it's the one that's suitable unless the question is specifically about phonology. I think in a language discussion those are likely, too, and distinct from the former.