I'm not sure if I used the correct terminology, but no matter what trickery they use, there's no way HackRF could receive the whole 1 MHz to 6 GHz range at once. Not even a "small" fraction of that, even if they somehow found a way to get a bit more than 20 MHz.
Its ADCs and processing hardware are not capable of that, and if the 5999 MHz of bandwidth were transfered to the computer with 8-bit I/Q samples, it would also require 96 Gbit/s of data transfer capability which is many times more than what USB 3.x can provide.
In order to show a larger slice of spectrum than 20 MHz, it still has to sweep over the desired frequency range (tune in steps repeatedly), like the RTL-SDR has to. It can receive a larger slice at once of course. And I don't know if it can tune quicker than RTL-SDR.
With fast sweeping the spectrum can look almost like real-time even though it isn't.
In fact, I'm not sure if there are any SDRs that could receive around 6 GHz in one bunch. Per Vices Cyan can do 3 GHz per radio chain with its high-bandwidth option so it could show 6 GHz of spectrum continuously with two radio chains. Or with the standard 1 GHz option, with six radio chains. But it might still be unable to receive a hypothetical 5 GHz wide transmission for demodulation and decoding. Merging two or more chunks of spectrum like that is not at all trivial in practice, as far as I undertand it.
Aaronia Spectran Enterprise models can apparently receive 1500 MHz per radio chain at once but I see them being advertised with "only" 3 GHz of real-time bandwidth. So perhaps they can't run four chains simultaneously on their full capacity. I don't know.
Per Vices Cyan costs more than 100 000 dollars, and Aaronia's flagship products aren't probably much cheaper.
@spongella
The sensitivity issue sounds like what I have heard about the HackRF. I do not own one so I can't comment more about that.