Hi, Walter -
I've extensively used the Dyson system, the Hoover system, and the Vax system, so I feel relatively well-qualified to answer your question!
In my opinion, Dyson's system is the most efficient, and with good reason; it's been improved continuously over 30 years, and Sir James and his army of design-engineers have already developed and patented all the best technology. Dyson Root Cyclone technology is protected by no less than 820 patents.
However, both Hoover and Vax have made very reasonable attempts at developing systems which do approach the efficiency of Dyson's.
I think that after Dyson, Vax's 'No Loss of Suction' system seems to be the next-best contender. At least, after continuous use in a number of houses since I acquired it in February, the pre-motor filter of my Mach 7 remains relatively dust-free. Wondering if the fine dust had simply passed right through the filter, I took the cleaner apart, and wiped around the inside of the motor-casing with a black cloth. There was no trace of fine dust inside the compartment, or in the air-ducts. And the post-motor filter was only discoloured by a slight trace of carbon emissions.
Hoover claim 95%+ separation-efficiency for their 'Airvolution' design. In practical terms, this means that 5% or less of the total volume of dust picked up should go through to the pre-motor filter.
However, after a single use, the Hoover's pre-motor filter is noticeably more discoloured with very fine dust than either the Dysons or the Vaxs'. To demonstrate, here are a few more photos. When I took the photos I've posted above yesterday, I cleaned all the parts as I went along, then washed both the filters. Today, I've used the Slalom to vacuum my grandparents' house. It got about an hour's use, and covered 8 rooms. The dust reached, but did not exceed, the max line.
Despite the dust build-up, however, I must stress that there was no appreciable drop in cleaning performance.
Dust in the chamber...
Tipped out on an A4 sheet of paper...
Unsightly dust...clinging fluff...damaging grit...
Fine dust, a few grains of grit, and a strand of hair, which have passed through the system...
And finally, the fine dust on the foam filter, which sits underneath the HEPA filter.