I would expect any issues dealing with seating depth, bullet type, velocity, etc to show on the target vertically, since that is the primary direction of barrel whipping.
Horizontal pattern is usually shooter issues; trigger pull mostly, maybe cheekweld or not holding hard.
Barrels vibrate in every direction. Where the muzzle is when the bullet exits is the where accuracy is determined.
The muzzle will "whip" in a figure 8 pattern as the barrel vibrates. Your best accuracy is going to be found on the smaller circle of the figure 8. If you use Dan Newberry's "Optimal Charge Weight" method you can usually find that particulare "accuracy node" in your rifle with a given set of components.