The effects of uniaxial strain on alpha-(BEDT-TTF)(2)MHg(SCN)(4) [M=K, NH4] were systematically studied in order to clarify the difference of the electronic properties between K-salt and NH4-salt. Superconductivity like NH4-salt was induced in K-salt by the c-axis uniaxial strain, while the density wave state like K-salt was induced in NH4-salt by the a-axis uniaxial strain. The latter was confirmed by the angle dependent magnetoresistance measurement. It was found that the ratio of the in-plane lattice constant c/a plays a key role in dominating their electronic properties.