Important thing is Regulation, not linear or switching type. Poor regulation in any of the two types can cause malfunction or even failure of the equipment which is being powered. It is the Section B of the power supply adapter in the flow chart below which determines the quality of power supply.
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LINEAR type power supply adapter
AC >> Section A (ac to 5V dc converter, linear type) >> Section B (regulator) >> dc output. -
SWITCHING type power supply adapter
AC >> Section A (ac to 5V dc converter, switching type) >> Section B (regulator) >> dc output.
The main advantage of switching type over linear type is that switching type has higher efficiency, generates less heat, and is lighter than linear type of same rating.
The main disadvantage of switching type is that it generates more RF noise than the linear type