I recently went through an airbrushing phase where I was trying different airbrush foundations and airbrushes, but to use these, one requires a compressor!
I bought a Dinar set (www.airbrushmakeup.com), an Obsessive Compulsive Cosmetics set (www.occmakeup.com) , and a Temptu set (www.temptu.com).
The Dinar compressor is loud, and very grating. It has an air pressure dial (regulator) on the compressor, and it's a fairly small unit. The unit cannot be used with dual action airbrushes, so that's a bit of a bummer (the booklet says it will void your warranty if you do so). It does produce a more continuous flow of air than the temptu/occ compressor (in my subjective opinion, not by any sort of scientific measurement). it's not exactly smooth air, but it's not bad. It also has a airbrush holding loop. The hose is just a rubber one, so it can only use the wedge type connectors, not the standard screw on type.
The Temptu and OCC compressors are the same. They are rebranded sparmax bakery type compressors. They don't really produce good air flow, but they are less noisy, and are very portable. They come with a case, and a battery so it can be operated away from a outlet. The OCC compressor comes with both an AC adaptor and the battery charger. The Temptu version only comes with the battery charger. They both come with the sparmax sp-35 airbrush which is a dual action airbrush, so I assume the compressor can be used with dual action brushes. The brush is decent, but the lever is a little bit jiggly which I don't really like, but that's for a different post :)
Between the two compressors I prefer the Sparmax compressor for a few reasons. I like the fact that it comes with a braided nylon hose, with standard connector. That means I can use any airbrush with it. I also vastly prefer dual action. Most of all, it's important for me that the compressor produce less noise.
However, if noise doesn't bother you, and you don't really prefer dual action brushes, then the Dinar compressor is prettier :) It comes in many colors you can choose.