To answer the question in the title, I don't think we have to choose just one.
However, my experience as Jehovah's Witness was that I must deny my feelings to do what is right. Supposedly, we arrived at what is right logically by determining what God wants us to do. If my feelings contradicted that, I had to ignore them.
Now I'm more free to follow my feelings. Personally, I think logic is still a much more reliable basis for decisions. Feelings, emotions, passions, etc. lead people assault and kill. Of course, some people say logic does the same, but generally I think logic that leads to undesirable behavior is usually false logic and can be overruled by logic. For example, the false logic that leads people to think that Jehovah's Witnesses have the correct interpretation of the Bible is easily defeated when considering more than the narrow set of facts they would have you consider.
In any case, it is good to be in touch with one's feelings. I try to pay more attention my feelings and the feelings of others now. However, in my opinion, logic and rationale will always overrule feelings.