Ecell is related to dH of a redox reaction. the more exothermic the redox reaction, the more energy you can get from the reaction when you set up the electrochemical cell. the current you get from the electrochemical cell would depend on: 1. the amount of energy released per mole of reaction, 2. the rate of reaction (this decides rate of heat released) 3. surface area of your electrodes 4. concentration of reactant and product species.
The nerst equation relates concentration of the oxidised and reduced species with respect to the Ecell value. Google for "nerst equation, electrochemistry"