Choosing between the two approaches is not a single test but a weighing of several criteria at once. The criteria that have accumulated across this course are: what kind of data you have (structured or unstructured), how much of it there is, whether you can afford the compute, whether the decision must be explainable to a person or a regulator, and how much the task is expected to change over time.
Take a concrete case. A hospital wants a model that flags patients at elevated risk from a routine blood panel, using a table of measured values from several thousand past patients. The data is structured and modest in size, the decision affects a patient's care and therefore needs to be justifiable to a clinician, and the panel of measurements is stable. Every criterion points the same way: a traditional model fits. It will train quickly on the existing table, its reasoning can be stated in terms of the measured values, and no specialized hardware is needed.
Now change one thing. Suppose the same hospital also wants to detect early signs in chest X-ray images. The data is unstructured, the collection is large, and the relevant visual patterns are not something anyone can name in advance. Here the criteria point the other way: a deep model is the realistic choice, and the hospital accepts that individual predictions will be harder to explain and that the training will need substantial compute. The point of working through cases like this is that the criteria rarely all agree, and the decision is made by weighing which ones matter most for this particular use.