I run my airbrush on a large tanked compressor intended for automotive tools. It's super loud so I run it on a 50 foot hose from my garage. I don't run a moisture trap on it - I never have moisture issues with it. The only issue I have run into is tuning the air flow rate can be very tricky- since I have such a long hose that also holds pressure it can swing wildly if adjusted incorrectly.
i have a badger brush. It's fine, tho I have no baseline for comparison