I know many on here claim to change axis tilt and axis rotation at will. But, if you can't do both, which of the two would you prefer to have the ability to change at will?

Rotation for me.

I am going with tilt. I have been trying to learn how to throw like some of my fellow league bowlers who have higher tilt than me. As I start to struggle, they are just starting to string strikes together.

 

Axis rotation.  Too much tilt tends to make the ball skid entirely too far on flatter conditions.  Too much axis rotation is easier to deal with.  Tilt is determined by how your hand is turned at your wrist and how early your thumb comes out of the ball.  It is measured most accurately by determining your track circumference.  Axis rotation is how far the holes are turned left to right when you come out of the ball.  If your holes are turning directly forward you would have 0 degrees axis rotation.  If your holes were rotating directly toward the wall and the side of the ball was facing you that would be 90 degrees of axis rotation.  Pete Weber's distinct and excellent ball roll is a product of 90 degrees of axis rotation and little to no tilt.  His ball still clears the front and reacts down the lane on almost any condition.  That is one of the reasons he can match up when few other bowlers can.

Correct...sorry the more tilt the further the ball goes down the lane...the less tilt the earlier and more consistently the ball reads.