The main differences are perhaps practical not conceptual. Drawbridge and Bascule are closed source. Grapheme attempts to implement a Linux compatible OS, from

The main differences are perhaps practical not conceptual. Drawbridge and Bascule are closed source. Grapheme attempts to implement a Linux compatible OS, from scratch, which is a huge task. Rump uses unmodified NetBSD code (kernel and libraries), so it is exactly compatible and updated continually as it is upstream in NetBSD. Also rump is BSD licensed, Grapheme is GPL, which is useful as you have to link it to your application.