Well the DC07 filter should be cleaner than the DC04 one, maybe the DC07 cyclones need jet washing internally or something
Also, i depends how old the DC07 is. IF it's a really late model with a number 2 by he oulet hole i's a cyclone where the filers stay cleaner for longer. Earlier models dont have as efficient cyclones for some reason. They may have no number or a number 1 by he rubber seal in the same place.
I had a 2005 DC07 ORigin with a number 2 cyclone which was de rooted (large holes at the top of the cyclone to prevent clogging). We used that as our main vacuum every day for a few months and the cyclones were fantastic, the filter was spoless. I then decided to vacuum Shake N vac (not recommended)and the filter had some white powder on it afterwards from he fine dust of the freshener.
Furthermore, the DC07 has a more powerful motor than the DC04 which produces more suction also. his means more air is being spun into he cyclones and a lot faster wiht the DC07 and the DC04 so I would say the DC07 is definitely better than the DC04 in pretty much every way (except the weight, noise level, bin capacity, post motor filter surface area and the weak bin flap pins & cyclone handle) Apart from that it's one of the best bagless vacuums in history every since bagless vacuums have come out
PS I like your profile picture! Really nice