Contact Form 7 is the more common of the two in our index: it runs on 974 websites against 23 for Embed Optimizer, and 4 sites use both. Counts come from real scans, not vendor claims.
Contact Form 7 is an WordPress plugin which can manage multiple contact forms. The form supports Ajax-powered submitting, CAPTCHA, Akismet spam filtering.
Performance plugin from the WordPress Performance Team, which optimizes embeds by lazy loading them only as they come into view.
4 sites run both Contact Form 7 and Embed Optimizer. That is 17% of the sites using Embed Optimizer, the smaller of the two.
Want to know which one a particular site uses? Look it up and see its whole stack, or compare two sites side by side.