Math or Physics: Which is the more relevant background to enter Cognitive Sciences and Psychology? What would be a more suitable background to enter cognitive sciences, mathematical psychology, and study of emotions? I have the option of taking a Integrated Masters Degree in Mathematical Sciences, or Physical Sciences. Going into which field will allow me to contribute greater to the study of the mind? Also, which field gives me more research options for the same?
I would go with Physics.

Physicists study the world using mathematics, while mathematicians study mathematics itself which is a construct that does not necessarily exist in the real world (Albert Einstein once said: "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."). This means that physicists encounter the interface between theory and experimentations, just like cognitive researchers, while mathematicians do not.

I think this is the reason why there are many examples of models developed in the study of Physics being applied successfully in cognitive science (e.g The famous Hopfield model (1982); Spin-Glass, Amit et al (1985); Ornstein-Uhlenbeck, Heath (2000); Diffusion, Ratcliff et al (2004) ). Obviously, all of these examples use math heavily. But while a mathematics student would study them using a theoretical approach, a physics student would probably study them emphasizing their application. 

(PS. My bachelor's degree is in Math, Physics, and Computer science, so I think I can say I'm unbiased here... At least I hope so)

References


Geometry and Experience, a lecture by Einstein A. English translation HTML
Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8), 2554-2558.
Amit, D. J., Gutfreund, H., &amp; Sompolinsky, H. (1985). Spin-glass models of neural networks. Physical Review A, 32(2), 1007.
Heath, R. A. (2000). The Ornstein-Uhlenbeck model for decision time in cognitive tasks: An example of control of nonlinear network dynamics. Psychological Research, 63(2), 183-191.
Ratcliff, R., Gomez, P., &amp; McKoon, G. (2004). A diffusion model account of the lexical decision task. Psychological review, 111(1), 159.