In British English you might use 'of' for a specific thing, eg. a book or person, and 'on' for a broad topic, eg. 'your opinion on string theory'.
But it's not a very strong rule, I wouldn't feel that either was wrong. This may be the effect of American English usage of 'on'.
To your specific question,
We surveyed drivers' opinion on this device?
of might be less ambiguous about whether you were talking about their opinion of the device, or you used the device for the survey. Does "We surveyed drivers opinions on twitter" mean you asked them about twitter or you used twitter to ask about something else?