As always, Orwell’s final rule applies: “Break any of these rules before saying anything barbarous.” There are instances where each of these words fills a valuable role. However, especially among inexperienced writers, these words are frequently molested and almost always gum up the works.
“Sudden” means quickly and without warning, but using the word “suddenly” both slows down the action and warns your reader. Do you know what’s more effective for creating the sense of the sudden? Just saying what happens.
When using “suddenly,” you communicate through the narrator that the action seemed sudden. By jumping directly into the action, you allow the reader to experience that suddenness first hand. “Suddenly” also suffers from being nondescript, failing to communicate the nature of the action itself; providing no sensory experience or concrete fact to hold on to. Just … suddenly.
Feel free to employ “suddenly” in situations where the suddenness is not apparent in the action itself. For example, in “Suddenly, I don’t hate you anymore,” the “suddenly” substantially changes the way we think about the shift in emotional calibration.