The first thing to get about either special or general relativity is that there is no such thing as the absolute size of objects, there isn't even absolute comparisons between the sizes of two things that are in relative motion (in special relativity), or in relative motion in two different places in a gravitational field (in general relativity). Thus one should not talk about things "getting longer or shorter" in some kind of definite, widely-agreed-on, "invariant" way. You see language like that a lot, but it's quite confused. Instead, relativity is about recognizing that if you compare the length of two objects, the answer you get depends on how you do the comparison, which is often called your "reference frame". Loosely, this means how you are moving relative to the objects (in special relativity), or where you are in a gravitational field relative to the objects (in general relativity).
Often, the two objects you will care about are a ruler that is in your hand, and some other ruler that is somewhere else or moving some other way. Then if you adopt standard conventions about how to make length comparisions (which means, more technically, choosing a standard way to coordinatize the spacetime, which in general means making a choice of a grid of observers whose rulers and clocks you will use to talk about the places and times where events occur), you will find that both in special relativity and in general relativity, you will reckon the other ruler to be shorter (if it is moving relative to you or at a higher gravitational potential), or longer (if it is lower in a gravitational potential than you are), relative to the ruler in your hand.
So I think your answer is, in general you must combine the effects of motion and the effects of gravity, and you must choose coordinates, to decide how a length comparison will turn out. The answer you get depends on your choice of coordinates unless you restrict to questions that deal strictly in the "invariants" (and length is not one of those, that was one of the big surprises of relativity).
