Laterally moving targets are difficult, but at most engagement distances, most centerfire rifles won't require a lot of lead. Out to about 200 yards, I'd think a 5.56 or a 7.62 would both be fine with a leading edge hold. I remember that working when I qual'd with an A2 and M855 ball, but that was a while ago.
This is assuming you're talking about typical walking speed of 2 to 4 mph.
Shooting uphill and downhill can also be tricky if the angle gets extreme enough. Both will cause the bullet to impact higher than Point Of Aim because the distance will be less than what the eye perceives it to be. It has to do with trig. Picture a right triangle. The elevation is the height. You see the target along the hypotenuse. But the actual target distance is the base, which is always shorter than the hypotenuse. So you may see the target being 400 yards away, but depending on the angle, it could be much closer, and thus, regardless of whether you're shooting uphill or downhill, the bullet will impact higher.
Within reason, however, this should make relatively little difference at most engagement distances and angles. The 5.56 and 7.62 are both flat shooting rounds, and humans tend to be vertical targets. A properly zeroed rifle with a BZO of 200 to 300 yards should still be inside the torso with a COM hold unless you're talking about extreme angles and/or ranges.
"...nothing says 'I WILL shoot every last one of you before you have time to reconsider your poor choices in life' like an AK."