I guess it should be NB .. the problem with weak signals is to distinguish them from noise. BB can't do that. And even NB can use time-averaging (it does not in DW).
But that is just theoretical and probably not-complete point of view.
Edit: hm .. here is argument for BB .. not all signals are harmonic - some of them are wide-spectrum noises. Like water flow for example and cavition noise too. These can't be detected on NB, at least not as lines. So target with great machinery and great silencing, where waterflow noise is more important (ie subs) could be favorable toward BB. But amount of these factors is unknown to me.
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