Camera sensors are the digital equivalent of a film frame and just like film, bigger equals higher image resolution.
A full frame sensor records the entire image that's taken into the camera through the lens. An APS-C sensor (Advanced Photo System type-C) only records a cropped portion of what's actually being seen by the lens.
As you can see there is a big difference in surface area. What this means is that a 35mm lens on a camera with a full frame sensor is recorded as a 35mm lens. A 35mm lens on a camera with a APS-C sensor will record only a portion of the image making the 35mm lens appear more like a 50mm lens.
Wider angle lenses work best with any type of stabilizer so having a 35mm lens actually work as a 35mm lens can be very important. If you've every used a video camera with a long lens or zoomed in and tried to keep the video steady then you already know that the longer the lens is the tougher it is. It can be like walking around while looking through binoculars as opposed to using the wide angle view of the naked eye.
This does not mean you can't use a camera with the APS-C sensor on a steady-cam and not get smooth results. I use a Canon t6i (APS-C sensor) with my SteadiGO and get beautifully stable video. Since my camera has a cropped sensor I use lenses from 28mm to 10mm when using a handheld stabilizer.