With the z-axis you're fighting gravity and all the weight is being supported on the leadscrew and nut. On the x and y-axis the weight is supported on the bearings. People often have the misconception the the z-axis will require less force because it weighs the least, but that simply isn't the case. No one will be able to tell you how well those motors will work without knowing the specs of the z-axis, weight, screw pitch, etc. but unless your machine is really heavy it probably wont be a problem.