A numerical model of photorefraction in barium titante with simultaneous hole and electron photoconductivity and combined deep and secondary photorefractive centers is compared with experimental observations of both continuous-wave (10 mW/cm2 -20 W/cm2) and pulsed high-peak-intensity (1-40 MW/cm2) laser illumination. Between 10 mW/cm2 and 20 W/cm2 (continuous wave) and below approximately 10 MW/cm2 (pulsed) the sample is hole dominated and has a sublinear intensity-dependent response time, whereas above approximately 12 MW/cm2 (pulsed) the crystal displays dominant electron conductivity and has a superlinear intensity-dependent response time.