The A350 & A380 (and all current Airbus airliners) use bleed air from the engines, just like all other airliners bar the 787.
The reason that people feel better after long flights on more modern aircraft like the A380, A350 and 787 than they do on older aircraft is due to lower cabin altitude and thus higher cabin humidity, which is largely down to the use of more composites in the construction, which can handle the higher humidity without corrosion problems. This better cabin environment is possible with bleed air or with electric compressors.
As an aside, the 787 also offers some protection from "fume events" (leakage of combustion byproducts or oil fumes from the engine into the cabin) since it doesn't use bleed air. However, there's still oil in the electric compressors so there's still some (much diminished) risk of fume events.
Before we worked out the issue (the risk of which really should be communicated by airlines) she was sicks for weeks after flying. And although unlikely, she once was caught in a fume event and couldn't work for months. Others on the plane were badly affected too. This is serious stuff and the 787 is great progress.
is that why the cabin of airplanes smell like jet fuel for the first few minutes of rake-off?
http://avherald.com/h?article=4b6eb830&opt=1024
The fuel smell at the beginning of the flight might just be happening because the engines and/or APU are ingesting the exhaust of the aircraft in front of you while on the taxiway, and some of that exhaust smell ends up in the bleed air that eventually enters the cabin.
A380 is relatively quiet but air quality isn't really comparable with the Dreamliner.