When comparing the different types of compression in Teradata, you must consider factors such as the data type and distribution of the column, the storage space and performance trade-off, and the compatibility and limitations of the compression types. For example, numeric columns are good candidates for ALC, while character columns are good for MVC. Compression can save storage space, but it can also increase CPU usage and affect performance. Moreover, not all compression types are compatible with all features and functions in Teradata. Therefore, it is essential to check the documentation and system requirements before applying compression to balance the benefits and costs of compression, as well as test the impact on queries and workloads.