Although it depends on the problem you are solving, but some general advantages are following:
Naive Bayes:
- Work well with small dataset compared to DT which need more data
- Lesser overfitting
- Smaller in size and faster in processing
Decision Trees:
- Decision Trees are very flexible, easy to understand, and easy to debug
- No preprocessing or transformation of features required
- Prone to overfitting but you can use pruning or Random forests to avoid that.