The ever-growing volume of data in imaging sciences stemming from the advancements in imaging technologies, necessitates efficient and reliable storage solutions for such large datasets. This study investigates the compression of industrial X-ray computed tomography (XCT) data using deep learning autoencoders and examines how these compression algorithms affect the quality of the recovered data. Two network architectures with different compression rates were used, a deep convolution neural network (D-CNN) and a vector quantized variational autoencoder (VQ-VAE). The XCT data used was from a sandstone sample with a complex internal pore network. The quality of the decoded images obtained from the two different deep learning architectures with different compression rates were quantified and compared to the original input data. In addition, to improve image decoding quality metrics, we introduced a metric sensitive to edge preservation, which is crucial for three-dimensional data analysis. We showed that different architectures and compression rates are required depending on the specific characteristics needed to be preserved for later analysis. The findings presented here can aid scientists to determine the requirements and strategies for their data storage and analysis needs.