First I think you get wrong conclusion in this: signal only consist of tonals. It's not true, it also consist of wide-band signals, ie noises. Those are hard to see on NB display but they add to total BB signal strength. This plays into BB sooner then NB theory.
Also you should use some different displays for NB .. those from matlab indeed does not look to good and the signal indeed can't be seen very well. Consider longer time window averaging which will cancel noise, also the noise in the sea is not uniform, nor are the tonals. So there can be many different situations.
If you had some really strong one high frequency tonal source, NB would help to differ it from mostly low frequenct background noise.
There is many BB sound sources in the sea. Only NB or aural evaluation can ID them as submarine.
I guess NB is first to identify contact as submarine. But BB could be first to make detection at all, with high false contact ratio. Also most books/movies follow this scenario.
But then I'm not submariner.
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