SYMPTOM:
After creating new compound MDX metrics or making modifications to existing MDX metrics, Strategy Object Manager Project Comparison functionality does not report these changes and therefore does not give the option to Replace the existing MDX metrics with their new definition in the destination project and does not move the new compound MDX metrics.
CAUSE:
Object Manager's Project Comparison feature does not support MDX objects. MDX objects should be migrated through the regular Object Manager interface as shown in the screenshot below:

However, MDX compound metrics are managed by the system, and therefore cannot be directly migrated across projects. If MDX compound metrics need to be moved then one should move the Reports that depend on the compound metrics instead.