WP Engine is the more common of the two in our index: it runs on 1,487 websites against 395 for Acquia Cloud Platform. Counts come from real scans of each site's home page, not vendor claims, and cover the sites in TechLookup's index rather than the whole web.
Acquia Cloud Platform is a Drupal-tuned application lifecycle management suite with an infrastructure to support Drupal deployment workflow processes.
WP Engine is a website hosting provider.
Within the paas sites we have indexed, Acquia Cloud Platform holds 0.9% and WP Engine 3.5%.
Want to know which one a particular site uses? Look it up and see its whole stack, or compare two sites side by side.