I think you're misunderstanding. Both are moving in time at the same speed according to the effects of both gravity and motion. Since according to Einsteinian physics the closer you are to a gravitational center the slower you move in time. Also the faster you travel the slower you move in time.

By moving an object away from the center of gravity (Earth) you are minutely moving it faster through time. But! The effects of being away from the center of the earth is negligable compared to the effects of traveling at high speed that slows it down.

Once one atomic clock is seperated from the other and placed in orbit it begins to move at a different rate through time. It's not much but it is measurable because atomic clocks are amazingly accurate.

So to answer you, neither atomic clock (you call them GPS clocks but I imagine you meant atomic clocks) is moving forward or backward in time. They are both moving forward in time at different rates, the one in orbit moves slightly slower through time then the one on the ground because it's slowing time as it approaches the speed of light.