As Yaya says, there are lots of different applications, for which there are many different solutions, at lots of differing price-points.
I am an architectural photographer and from time to time have to shoot buildings from choppers and also cranes. Here are some of my work practices, but remember, they are specific to my particular jobs.
I shoot all my aerials with my MF gear. In recent years, that has meant P65+, Aptus 12 and IQ180 backs on either my DF camera or more commonly, my Alpa STC. I also regularly shoot pseudo-aerials whilst suspended from crane baskets both from hi-rise buildings and from construction barges at sea (oilfields).
From choppers I usually use my 40HR Rodie on the Alpa or my 45 or 55 lenses on the DF. Anything longer is too susceptible to vibration. I always work hand-held, without a giro. I haven't yet found a giro that allows me the flexibility of movement I like. Other shooters wouldn't dream of shooting without a giro.
The type of helo you use is important. Small platforms like the Robinson R22/44 are boneshakers for vibration and with the door off, almost impossible to stay out of the downdraft. I refuse to shoot from them these days. The Bell Jetranger family are better and if you keep your camera high in the cabin, you can get right to the edge of the door and still be out of the downdraft. My faves are the Squirrels and Hughes 500 and all the recent Eurocopters. Stable, low vibration and lots of room to move.
My preferred option is the Alpa STC with the 40HR(downshifted about 12mm) and IQ180. I use it with the Alpa Sync adapter, turned sideways so I can fire with my left thumb. I've shot from choppers with shutter speeds as low as 1/125th, though I prefer to be at 1/500th where there is enough light. I never shoot at apertures wider than f8. When shooting from cranes, I usually use my 23HR handheld, at shutterspeeds as low as 1/15th of a second. Tripods are almost impossible to use in crane baskets due to the fact the basket never stops swinging and rotating, especially if it is windy. The German made cranes are much better than the Chinese ones commonly used in the Middle-East as they transfer less vibration to the basket. Needless to say, you need to have some confidence in the safety of the crane you are about to ride in. I've been up as high as 86 floors in Dubai, which frankly, was nerve wracking. I've also been on sites in India where I have flatly refused to ride their crappy cranes! Whilst this is not really directly a photographic issue, it does have some bearing on ones state of mind and therefore ability to perform creatively. It's hard to do great pictures when you are terrified! At sea, when the crane is mounted to the deck of a barge that is rolling on an ocean swell, the game is usually quite tricky as the basket is always swinging. On my last shoot at sea, the position of my basket was shifting about 10m relative to my subject and I could only shoot one frame at the end of each arc, when the basket was relatively still.
There are several examples of these images on my website,
www.bryansiebel.comCheers!