You will find that some tasks are suited to one particular method more than the others, but when you do a variety of modeling tasks, you realize that no single strict method is good for all tasks. 

Tasks like modeling tube shapes, e.g a neon sign or a pipe, naturally lend themselves to "spline" modeling (extruding a shape along a spline path).; mimicking the behavior of a machinist's lathe (typically called "lathe" in modelers); or taking a floorplan drawing made of splines and "lofting" walls from those splines.  All are fairly easy with different applications of spline modeling.

Tasks like modeling a box (duh) are well suited to box modeling; any task where you need a shape that has volume and is "watertight"; also there are many applications with strictly 2-d surfaces where you extrude the edges, e.g. in character or clothing modeling.  Good applications for box/extrusion modeling.

Tasks where you need exact control of the overall structure of a model are well suited to poly-by-poly modeling, e.g. when you're modeling a character's face and you absolutely must define specific loops of polygons for the eye and mouth; when you're using polygon snapping to start a clothing model that will match the shape of a specific character; or you need to model a specific flat polygonal structure like the sail of a boat.  These are good tasks for poly-by-poly modeling.

However as your models get more complex and detailed, you find that you need to use a variety of different techniques, and strictly constraining yourself  to just one method makes the job much harder.

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