I understand that you selected these terms intuitively, but now that they're on the table I'd like to hear you elaborate a bit on just what you mean by each. At this point, if I go by my fuzzy ideas about what I think you mean, I don't see how these can be considered exclusive or even distinct ways of approaching a decision.

Let's take "empathy." I assume by this you mean something to the effect that one's decisions should be informed by consideration of the preferences, rights, and feelings of those who would be affected by the decision. But it's not clear to me that this differs in a deep sense from "reason," given that the decision maker here is explicitly reasoning in at least two senses: (a) reasoning about what the other person's preferences are, what rights they are entitled to in this situation, and how the decision will affect their feelings, and (b) reasoning about the extent to which each available option would both respect these other-oriented criteria and also conform to the decision maker's own view of morality. It seems that you could easily say either that empathy is a component of reason, or conversely, that reason is a component of empathy. In any case I don't see that they are fundamentally different.

The distinction between "intuition" and reason does seem a little more clear to me, but again, it's not clear that these can be considered separate in every instance. There are decisions for which an analytic approach seems appropriate and decisions for which an intuitive approach seems appropriate, so it seems problematic to say that one should be considered overall "more important" than the other. For example, if I'm having unusual car problems and I'm examining my engine to figure out exactly what the problem is, it seems clear that a good amount of conscious, explicit reasoning and testing will get me a lot farther than simply declaring the problem based on my intuition and then proceeding to try and fix it. On the other hand, if I'm deciding which flavor of ice cream to put in my ice cream cone, it seems clear that there is little or nothing that "reason" has to say about this, and the best way to approach the decision is to consult my intuitive feeling about which sounds the most tasty. You might even say that consulting my intuition is the "rational" choice for this decision.

So as a summary, it's not clear to me that "empathy" should be considered something separate from reason or intuition. And while the distinction between reason and intuition does seem more defensible, it seems to me that whether one method should be preferred over the other depends entirely on the decision, so I would be hesitant to make a general statement that one is more important than the other. But maybe if you clear up what you had in mind when you came up with these terms we can come to a better understanding.

I find the general idea of reason/rationality vs. intuition/emotion extremely interesting. That is, it's interesting to me to consider the differences between the two and when/whether we should prefer one, and it's interesting to me that we dichotomize the two in the first place.