The difference between the two security features is that Safe Browsing will compare a visited site to a locally stored list of domains, compared to Enhanced Safe Browser, which will check if a site is malicious in real-time against Google’s cloud services.
While it may seem like Enhanced Safe Browsing is the better way to go, there is a slight trade-off in privacy, as Chrome and Gmail will share URLs with Google to check if they are malicious and temporarily associate this information with your signed-in Google account.
firefox does utilize the lesser version of these google-provided services by default–how it works
Firefox downloads a database of URLs to block. It doesn’t send every URL you open to Google.
It sends some though: