I think you maybe need to do some tests - maybe with a DSLR or something you own or can borrow
Firstly - stabilsation software - isnt really a solution I guess
the basic premise for this argument is that when there is a jump in the footage there is motion blur
Software cant correct that so even when the footy is stabilised there are artifacts
When shooting from vehicles there are three issues to battle
you might call them 'micro jitter' and 'unstability' and 'subject distortion'
micro jitter is picking up vibration ie frequencies from the prop propellor engine (harmonic vibration)
Unstability is large bumps caused by failure of the camera support system to react to accelleration - eg turbulence or change in direction
There is also jello in the image caused by rapid movement across the image subject - I guess this is not going to be a problem unless you are going really low and fast
In summary what I am saying is that choice of camera may not be the issue but understanding the stabilisation methodology may be
DSLR in motion by me - no stabilisaton in post
Car shooting.. http://www.vimeo.com/25351225
Hard car mount risk micro jitter
Steadicam is perfect but subject changes of direction**
Plane Shooting http://www.vimeo.com/10784709
Shoulder mount of the camera isolates the camera from the airframe but is subject to turbulence
Use of the 14mm helps 'turbulence'
Another consideration is the mass of your system - for example a GH2 has low mass compared to a video camera and may enable more ambitious solutions - ie lets say your system has to be rated to 2G the strenght may need to be 16th of the rig to support a 'video' camera
ie a gyro may
work far better with a GH2 than a vid camera
Also worth considering is IS/VR lenses which can do great things with certain types of movement - not harmonic vibration but directional change
I think you may not need to worry about the camera or certainly a video camera may not be part of the most affordable solution package
use of steadicam in helicopters is a well known "NO DONT DO IT"
Danfung dennis has done it however (see his afghan work) - using a glidecam - a tiny rig - and got great results