Heart & brain are the two main contending organs for definition of life & death. They are also the two contending organs in decision making. In decision making heart is usually associated with emotions. It's mainly for historical reasons even though there might be some physiological reasons. Brain is associated with logic. More specifically with verifiability in a mechanical way. Since the notion of computation unifies the concept of machine it means verifying in a computational way.
We know a lot of details of working of heart: at least to the extent of having mechanical hearts that can simulate the pumping blood which is the primary functionality of heart for life. While mysteries of brain are still abysmal, self-referentiality of thinking lead to computational model of brain which lead to the dream of artificial intelligence. Efficient computations are usually based on local information which limits its powers in this physical world. In fact the limits of logic as pointed out by Godel are based on the fact that logic is based on local information. In general the locality principle limits us from having God like powers. The more experience we gain the better is our global perspective. Hence experience helps!
Emotions are usually mysterious and quite "non-mechanical" to deal with. This hints us that we might be processing something more than local. We feel emotions instantly about someone miles away something like the famous "spooky action at a distance" phenomenon of quantum mechanics. The typical explanation of the "entanglement" behavior in modern physics is that the particles all belong to "same system" and that's why they are somehow "connected". Though they usually say this so that classical principles (like constancy of speed of light) of physics are consistent with modern principles. Thus there is something global happening with entanglements and hence hard to be verified mechanically. Hence for e.g. even though "heart-breaks" is a common term usually the mysteries of emotions are rooted in the brain NOT in the heart. This realization will atleast let you focus on using appropriate resources for specific problems. Specifically, when you are baffled with emotions you should rely more on brain to help yourself.
N.B.: Updated May 10, 2008. 1:36 AM.