Constituency vs Dependency Parsing: What is more effective for Sentiment Analysis?
Both approaches have been used for sentiment analysis in the literature. From a quick search, we can find these results:

Constituency parsing:

Deep Recursive Neural Networks for Compositionality in Language [NeurIPS'14]
Less Grammar, More Features[ACL'14]
A Statistical Parsing Framework for Sentiment Classification [Computational Linguistics journal'15]


Dependency parsing:

What's great and what's not: learning to classify the scope of negation for improved sentiment analysis [NeSp-NLP'10]
UBham: Lexical Resources and Dependency Parsing for Aspect-Based Sentiment Analysis [SemEval'14]



It seems to me that constituency parsing has been used more than dependency parsing. My sample, however, is very small and focused on the English language. I think this may change in languages with more complex (and more non-projective) syntax.
That been said, I think currently neither of them are considered to be state of the art in sentiment analysis. If we take a look at the leaderboards of sentiment analysis tasks from paperswithcode, all of the leading approaches (BERT, RoBERTa, M5) handle text as a mere sequence of tokens. While these results are from only a