I can't actually help you on differences between the Abraxas and Crawlers, I've not tried them myself - maybe someone else can?
On the "top end cutting through the bottom end", I think we're talking about the "clarity" or "openess" of pickups - always difficult to describe in words.
Across all BKPs, some will be darker and thicker, some brighter, etc. - they're designed for different jobs.
But in general, all BKPs seem to be more organic and open sounding than their non-BKP equivalents. In practice, this means that they respond really well tonally to your playing style - you can hear more of what you put in with your fingers - and you can hear all the frequencies they are designed to produce - you get the top end and the bottom end, etc.
I haven't seen this written for a while - the way that some people describe it is: "when you put BKPs in, you suddenly discover you can actually use the tone controls on your guitar" :D