Do White S2 and Grey S2's use the same version of TiVo software?

I've got a friend who has a grey front Tivo s2 with no HDD. I have a white front S2. Is the Tivo OS version on the white unit the same as would be on the grey? He wants me to copy the drive from my tivo to his, but I wanted to double check and make sure the image would be compatible...