You need to work out which criteria are important to you - looking at a new job, money and promotion prospects will be important to some people, whereas short commute and flexible hours might be more important to others. (This is all based on the assumption that no one job is perfect in all ways, because if it were, there'd be no dilemma.) Also, some criteria will impact others - for example, a well-paying job might have a longer commute and consequently higher travel costs, which reduces the effect of a higher salary.
I think if you are really struggling with head vs heart, you need to analyse why. Are there criteria you thought weren't important to you, but actually are? Is your heart''s decision based on reality, or how you'd like it to be? I mean, if you were considering moving in with someone, and on paper, you have discounted them because they're really bad at financial planning and housework - well, that's not likely to change much, and living with it is different from only seeing it at more of a distance. You'd need to think hard about whether all the positives are really worth penury and mess longer term, or the resentment of being the only one who does the clearing up. There are plenty of MN threads to indicate that isn't necessarily a good recipe for a long-term relationship.
There are other things where you really have no choice but to take a punt - revolutionary new medical procedure with long-term cure if it works, but poorer prognosis if it doesn't vs established procedures which won't be a cure, but have been proved to extend the time before a condition deteriorates - even the experts don't always know the odds on that sort of decision.
I'm not saying don't go with your gut, but I think you need to try and work out what it's based on, because gut instincts are developed at a subconscious level through past experiences and so on - they don't appear from nowhere.
Good luck!