Is it possible to measure the differences in processing and interpretation of reality between individuals?
The answer to this question is rather philosophical will mainly depend on who you ask.

If you ask someone who is close to physicalism, he would probably respond that there exists nothing that cannot be measured, hence, differences in the processing and interpretation are measurable in principle too, although we might lack the necessary apparatus and methods right now. 

However, if you ask some who is closer to dualism, he would probably respond that there are (at least) two kinds of consciousness: access-consciousness (or a-consciousness) which can be measured with scientific methods, and phenomenal-consciousness (or p-consciousness) which is only accessible to ones own mind and cannot be measured by scientific methods in principle (cf.  the hard problem of consciousness). 

Please note that this answer is a simplification that gives only a glance into a debate that filled volumes (cf. http://en.wikipedia.org/wiki/Philosophy_of_mind)