Mainly, which is actually better? I want to know which one to use for production and what are the actual differences between them. I'm going to be using Bootstrap in them.
Adobe Edge Code is a distribution of the Brackets open source project. It contains all the functionality of Brackets, plus additional extensions that integrate with other Adobe products like:
Edge Code uses the Creative Cloud desktop application to update in place. Brackets does not have an automatic update mechanism (yet).
As an open source project, Brackets releases new features more often, so there is a slight delay between when a feature lands in Brackets vs. Edge Code. Brackets also integrates with a central community-managed registry for browsing and installing extensions. Extensions must be manually installed into Edge Code.