I would not feel safe having a doc make a diagnosis with xrays on a potentially serious spine injury.
The CT has a significant amount more detail, allowing a radiologist to review the spine slice by slice up the spinal column, allowing them to review disc by disc. Also through one scan, you can see the spine from multiple planes (axial, sagittal, coronal, transverse) without having to toss the patient every which way, and the reconstructions can give additional insight.
Xrays by comparison only give limited overviews of the patient’s spine, and the quality is subject to technician tequnique, and the ability/willingness for the patient to cooperate. There isn’t enough detail there to ensure that something won’t be missed, especially if it’s a small fracture.