I have never used stabilized binoculars but I could see they handle the issue of shaking.Let me introduce you to Kite Optics and their stabilized binos that are just great, had a play with them in January on a pre-production model. You can even id a bird from a rocky boat, there are 2 models, a 14 x 50 and a 18 x 50 and either with AA batteries or with build-in Li-Ion battery. I do have a Swarovski but seriously considering a switch.
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APC Stabilized 50 - Kite Optics
Introducing the astonishing APC 50 Image-Stabilized Binoculars. Experience KITE OPTICS’ KT3.0 image stabilization technology through our most powerful 50mm ED optical system. Designed for precision and sharpness, these binoculars redefine your observation in every way.kiteoptics.com
For bird photography use I am less interested in being able to get close to a known bird so I can identify it, than I am in finding a bird I might be able to approach close enough for a shot.
My problem with higher power binoculars is not so much the shaking, but the narrow field of view. Just like shooting with a long focal length lens it is harder to get the image into the viewfinder. I actually prefer to work with an 8 power binocular because it is easier to scan through a larger area to see what might be out there. My 8 power binoculars have to have super sharp resolution and a bright image.
Any bird I can't make out with a QUALITY 8 power optic is likely to be too far away to photograph.
I have been using a 15 year old pair of 10x42 Leicas that at the time I bought them were the top of the line. They are still incredibly sharp although no longer state of the art. I recently bought a pair of Maven B.1.2 in 8x42. The Mavens are really sharp and have a clear bright image. They are also lighter weight than the Leicas. The Maven simply works better for me on a photo shoot. I can scan a wider area, I have less eye strain and I can easily spot what is out there.