I've only owned one of the two, but I've always been under the impression that the Crawler is like a super-powered PAF (more vintage voiced, as badgermark says) whereas the Holydiver has both feet in the hard rock/metal camp, without being a full-on mega-output screamer.
In my LP the Crawler was very fat with a real growl to the tone. My impression is that the HD is also a fattie, with lots of low mids but, perhaps, a smoother, somewhat clearer tone(?)