The HP00 and HP03 are similar, the HP03 is able to link to the Dyson Link app, hence the word link in the name. The HP00 & HP03 don't come with the LCD screen that your HP04 has. The oscillation of the HP00 & 03 are limited at a 70° angle i believe, while the HP04 has a wider oscillation Your HP04 comes with a diffused mode for when you don't want the fan. Also the filter of the HP04 is better. It is certified asthma and allergy friendly as it is sealed (so minimum leakage). The HP00 doesn't come with sensors as it doesn't show the Air Quality reading. The 03 has a sensor that shows the AQ when connected to the app. The sensors for the HP04 are more advanced as it shows in detail the different pollutants that is sensed. I might have missed out some but i think that's pretty much it. Minor details here and there.

Thanks so much for this response. It was great. 

Sounds like the HP04 is superior on enough fronts to make it the standout choice for my next purchase. 

Ugh, looks like they don’t sell the HP04 any more. I guess the HP07 or HP09 would be the next best options.

The HP07 replaced the HP04. The HP07 and HP09 are similar, the only difference is that the HP09 has an additional filter, the SCO(Selective Catalytic Oxidisation Filter). This filter is a lifetime filter which captures and destroys a chemical called formaldehyde. Formaldehyde is usually present in an unhealthy amount when there is renovation done or if you've just moved in to a new place. Reason being this chemical is released from things like plywood, new furniture, paint, carpets and many other household items. This filter is great when it comes to dealing with large amounts of Formaldehyde. Small amounts of this chemical can be filtered by the carbon filter which is also present in the HP07 and other purifiers with the carbon filter. Formaldehyde will fall under the VOC category in your HP04/ HP07.