I will make an attempt but I am retarded and ignorant towards both. Also, as ZapperZ alluded to, Quantum Mechanics encompasses both an experimental aspect of physics and a theoretical aspect. You need to perform experiments to verify theories. Mathematics does not accurately reflect reality. It is physics which uses the language of mathematics, to model and describe reality. Even the most cutting-edge theoretical physics, requires some form of predictive power in order for it to be considered interesting. String Theory is perhaps the only exception to this rule. As far as I know, it has not made a single useful prediction (other than what we might discover at CERN this year) and has no empirical basis.
When I consider the experimentalist, my concept is of someone who is verifying potential mathematically modeled theories, by constructing experiments that will allow for the empirical testing of specific predictions.
When I think of a theoretician, I imagine an individual who constructs mathematical models and complex simulations, describing a particular phenomena or property of the physical universe. They make predictions so that the experimentalist can verify them.
An experimentalist does a bit of 'theoretical physics' in the sense that they have to creatively construct an experiment, that will successfully and accurately verify or falsify a particular prediction or even an entire theoretical model. The experimentalist tends to rely on the theoretical physicist for predictions to test. A theoretician creates models and/or simulations of a particular phenomena (or perhaps entire universe), which makes particular predictions for the experimentalist. There is a bit of 'experimental physics' involved, in the sense they tend to try out and experiment with different equations, maths, models, etc. The theoretician relies on the experimentalist to test their predictions, in order to empirically verify or falsify their intuition.
It's an elegant relationship, in which both roles are equally important and compliment one another. Experimentalists tend to perform more 'hands-on' work, while the theoretician tends to perform more 'thinking and writing' work.
ZapperZ will, of course, provide us with a more definitive answer, though! That's because he secretly loves us. Atleast, that's the cognitive representation that I have engineered based on my readings of Popper and Kuhn.
. It could be argued that nature is perfectly mathematical and difference between theory and experiment is only due to inaccurate assumptions and and inability to retrieve all existent data.
