Recently, the new research field of room temperature liquid metal cooling for extreme heat flux electronic devices has gradually attracted much attention. And many investigations claimed that liquid metal cooling has a better heat transfer performance than water cooling. However, such a conclusion was just applicable to the special geometry sizes. This paper is dedicated to deeply interpret and systematically compare the laminar heat transfer in a mini/micro pipe with water and liquid metal as heat transfer fluid. Theoretical analysis for the laminar fully developed segment and numerical investigation for the laminar developing segment were conducted. The results indicated that liquid metal galinstan shows a better heat transfer performance in mini-pipe. And the shorter the pipe, the better performance the liquid metal cooling has. However, when the velocity is small, the galinstan cooling is worse than water cooling in micro-pipe. Moreover, based on thermal resistance analysis, the general criterion equation for laminar developed segment was derived to judge which cooling method possesses a better heat transfer performance. Overall, this comparative study provides a comparison method and criterion about liquid metal cooling and water cooling, which will attribute to the coolant selection and heat sink design.