Epitaxial BiFeO3 thin films have been grown on (100)-oriented SrTiO3 and Nb-doped SrTiO3 substrates using the pulsed laser deposition technique under identical thermodynamic and variable kinetic conditions. The variation of growth kinetics through laser fluence and pulse repetition rate had minimal effect on the structure and magnetic properties of films. However, large changes were observed in the microstructure, with initial island growth mode approaching toward step-flow type growth and roughness reducing from 12.5 to 1.8 nm for 50 nm thick film. Correspondingly, the leakage current density at room temperature dropped consistently by almost four orders of magnitude. The dominant mechanism in low leakage current films was space-charge-limited conduction. These findings suggest that the issue of leakage current can be dealt favorably by controlling kinetic growth parameters. The application of high electric field and observation of maximum polarization value up to 103 μC/cm2 could be possible in these samples. An appearance of saturated hysteresis behavior depending upon bottom electrode was also observed. This fact is qualitatively explained on the basis of recent concepts of switchability and polarity of thin film-electrode interface.