When is modified duration enough, and when do I need convexity too?

Modified duration is usually enough when the prompt gives a small yield change and does not provide convexity. It gives the first-order linear estimate. Convexity becomes relevant when the prompt provides convexity, the yield change is large enough for curvature to matter, or the question explicitly asks for a more accurate price-change estimate.

Think of duration as the slope and convexity as the curvature. If all you have is the slope, use the slope. If the prompt gives both slope and curvature, use both when estimating the price change for a meaningful rate move.