The precursor influences on Ni/Co metal–organic frameworks’ (Ni/Co-MOFs’) structure and electrochemical performances were studied, and highly enhanced Ni/Co-MOF nanosheets was obtained from a nitrate precursor and named as MN. Compared with the Ni/Co-MOF nanosheets obtained from a chloride precursor under the same concentration (labeled as MC), the nitrate developed MN exhibited a much thinner and cross-arranged nanosheets’ structure, which contained a higher Ni/Co ratio (MN, 1.82; MC, 1.47). These structural differences led to totally different electrochemical behaviors. At 1 A/g, the MN thinner nanosheets showed a superior specific capacitance of 2860 F/g, which remained above 90% after 2000 cycles. On the contrary, the MC thicker nanosheets had a maximum specific capacitance of 1350 F/g at 1 A/g, and it decreased to around 47% after 500 cycles. With an energy density of 88.84 Wh/kg and a power density of 750.89 W/kg, the MN thinner nanosheets also performed well in asymmetric solid-state supercapacitors.