It depends what you mean by their clocks both being at noon when they're at positions A and B, and their speeds differing by 161,000 miles per second. By the way the question was stated, I'll assume you meant their positions were measured in an outside observer's frame, i.e., at noon in the outside observer's frame ship A is at position A and ship B is at position B. We can also assume ship A sync's up its own clock to read noon when it's at point A, and similarly for ship B. (It is impossible for both ships to see both clocks at noon at once. If ship A sees both clocks at noon at one time, then ship B won't, and vice versa. Specifically, if ship A sees the event of itself being at point A (with its clock at noon) coincide with the event of ship B being at point B (with its clock at noon), then ship B will not see these events coincide.)
As for what frame their relative speeds are measured in, it sounds like you meant the ships' frames, i.e. ship A sees ship B moving towards it at 161,000 miles per second, and ship B sees ship A moving towards it at 161,000 miles per second. Then the $\gamma$ factor between the two frames is about $2$, meaning time appears to move half as fast for one ship as measured from the other. Unfortunately, having specified their relative speed in their own frames doesn't specify it in the outside observer's frame. This is what matters, since the outside observer's frame is the frame in which both their clocks were seen reading noon at once.
If one ship is moving faster than the other in this frame (the outside observer's frame), then its clock will elapse less time than the other's.
