Diffy has custom intelligent image comparison algorithm that recognizes vertical shifts. Both BackstopJS and Diffy have abilities to hide / remove elements from the page, scroll, delay taking screenshot and running custom javascript.
With BackstopJS you'll need to install tool locally and you are limited by your computer's resources. With Diffy you start immediately on highly scalable infrastructure based on AWS Lambda.
We have spent a lot of time refining our UI for large number of screenshots. Diffy has a thumbnails view and detail view with zooming option while BackstopJS shows all screenshots one under another (that can be grow a lot vertically)
Diffy has CLI tool and rich REST API that make CI integration like a breeze. Also, you don't need to worry about where to store results -- your team can go to the app and do the review. There are shareable report links so your team members or clients don't even need accounts in Diffy to see them. Diffy can post results to SLACK and send notifications by email. In case of BackstopJS you will need to take care of all these on your own.
BackstopJS by default allows you to take screenshots and compare them with the baseline. While Diffy also can do that, it provides you with possibility to have multiple environments and keep the history of screenshots and comparison reports.