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Always continuous!
Assuming you are trying for a predictive regression, that is. Compressing to 0/1 is throwing away information, plus it gives you many more opportunities to overfit as you will be tempted to choose the threshold to get a good result.
Only reasons for using dummy variables are (a) you have a categorical (unordered) variable that you need to encode (b) the feature is essentially two-class anyway (e.g. very bimodal distribution) and you don’t think the variations around the peaks add any information.
Discretising continuous variables can also lead to jumps in your forecast if the underlying variable meanders around the threshold over time, which lead to undesirable turnover in your strategy (which costs you money)
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