I heard that Xtext ultimately uses ANTLR but their grammar specification files have somewhat different formats. So what's the relationship between the two?
Xtext relies on the Antlr parser generator for the parsing of input files. On top of that the framework provides lot's of added value such as strongly typed ASTs, abstractions for linking and static analysis as well as IDE integration for Eclipse.
For that purpose, Xtext generates two Antlr grammars. One for the production parsing where the actual AST is produced, and a second grammar that is used to consume events to compute the content proposals for the Eclipse editor.