It probably has less to do with the computer and more to do with the 32-bit exposure setting - it's probably set differently between the systems. 32-bit files contain more data than your monitor can ever display. The 32-bit exposure slider lets you 'preview' tonal data you have to work with.
This slider only affects the on screen preview. You're not tone-mapping the image at all with this slider. If you want to control how you image appears, use the tone mapping features in Photoshop or Camera Raw to produce a 16-bit or 8-bit image for your screen or print.