They're all the same thing, at least when they count.
Basing your decisions on good thinking is always a good plan and you can simply never go wrong with that. But good thinking isn't just hard logic. It's paying attention to emotion -- yours and others' -- among other things. "Following your heart", that is, paying attention to what you want or feel is right, is a core part of using your head. I could determine that one way I could do something is more difficult... but if it sounds like more fun, how is it a bad decision?
As for gut instincts... I don't believe people just magically have an internal instinct that feeds them good or bad ideas (depending on the person). All I think a gut instinct is, is a subconscious evaluation of facts or bits of information that you haven't noticed on a conscious level. I always listen to my gut because it's pretty much never wrong; times when I've ignored my instincts and tried to reason them away always have turned out badly for me. This isn't true for everyone as this works different depending on the person; someone else might not function as well subconsciously (or in general, sometimes) as another person, or some other people might evaluate more consciously and not need the subconscious evaluations. Bottom line though is I simply don't believe the gut instinct is completely separate from the intellect; how could it be, if, for some people such as myself, it's usually accurate? Accuracy requires understanding. Evaluation.
So bottom line is they're all different facets of the same thing. I would never say I depend the most on my gut, because I follow all of my instincts with conscious evaluation -- try to pick apart why I have that gut feeling -- and of course evaluate things regardless of whether or not my gut tells me something is up with them. But regardless of whether I'm thinking consciously or following my instincts, my "heart" still factors into it; what I want to do, or what I feel I should do, are both still evaluations.