You should check wether both cameras are metering the same exposure value. (have a look at the exif's). If yes, the manufacturers have different definitions of the "ISO" value. On the other hand every lens have a different transmission of the light, therefore in the video camera word they a using the T-Stop value. With a T-Stop two lenses with the same value put the same amount of light to the sensor
Wikipedia: A
T-stop (for transmission stops, by convention written with capital letter T) is an f-number adjusted to account for light transmission efficiency (
transmittance). A lens with a T-stop of
N projects an image of the same brightness as an ideal lens with 100% transmittance and an f-number of
N. A particular lens' T-stop,
T, is given by dividing the f-number by the square root of the transmittance of that lens: