I have just solved this problem.
Yes, we do. Unless there was a machine which could replicate you exactly, we all experience different sensations when sensing the same thing. We also have different understandings when we think about the world around us, because we don't learn in exactly the same way. We may come to the same step by step conclusions, but the actual process in the brain will not be the same.
However as we experience the same colours and tastes etc in the same way as we have in the past, this suggests there are some continuous properties to experiencing something in different states of mind. The way our brains work are very similiar, especially our senses and emotions which are not affected by the environment much, though not the same.
Different brains through time is one thing (your brain when you were 5 and your brain now), but different brains will be different in their properties as they are composed of another set of substance.
One thing we are all aware of is the difference between pleasure, pain and our evolved responses to these stimuli, however we will not experience the same colours as someone else, we can look at the same colours, just not experience them in the same way.