Always a hotly debated subject. But I go for Dyson. And for good reason. This is something I have experienced with our demo machines, we demo with sand, sawdust and cat hair.
The brands we represent:
Hoover: Typical pleated filter in budget models. The globe appears to have a design flaw, dust leaks from the lower half of the bin to the top half where the cyclones are. Not reassuring.
Vax: Pleated filters for basic models. Even the Air is poor. The Air Max Pet was demoed with cat hair, only found to be deposited on the filter.
Bosch: Again pleated filters. Not had much to do with these.
Samsung: Single cyclone and multi. The multi separation is poor, especially noticed on the upright. Sand leaked it's way through, and fine dust on the filter.
Shark: Single cyclone, very poor. Not sure how they get away with no loss of suction. The demo machine has a filter covered in dust, sand in the filter cavity.
Dyson: All demo filters clean. Washed on the odd occasion.
The point here is that Dyson have the best separation system available, even amongst multi-cyclonic. Dyson machines are demoed more than the others yet still have clean filters.
Given we only demo the machines for five minutes with a handful of dirt, I dread to imagine the efficiency of these machines in real life use.