For me, this is like a question from hell...
Type, theoretically, should absolutely be the winner. It's just that personality type systems are often so riddled with problems or applied so incorrectly that they tell one nothing at all. Personality type is one of those frustrating things where we can know something is knowable, but not know how to know that thing. Not yet, anyway.
With gender, there is possibly some merit in making a guess about someone's personality based on it (as much as I hate to say it) if you have a good understanding of the culture of the person you are dealing with. Biological differences aside, genders are conditioned differently everywhere. This means that when comparing gender assessment could be more affective than any number of completely awful personality type systems.
But really, if you can hold a personality type system up to some basic standards in its design and application (something that has been surprisingly hard for people to do), it should be more accurate because it should reflect details about the mind of the individual being typed, and that's more reliable because (here we go again) even if you swallow all the purported evidence of gender differences, individuals within a gender are on average more different from each other than the two genders are collectively different from each other.
And the usual disclaimer follows that if you are trying to do a case study of someone, you can probably just forget about gender and personality type. They might hurt you more than help you in understanding all of a single subject's potentially deviant nuances.