I am not sure if for the same shutter speed, aperture and ISO there would be such a big difference in shutter speeds.

The implementation of ISO by camera manufacturers is different. So even though two cameras may show the ISO as 100, in actual case the ISOs may be less than or more than 100. The focal length equivalents also vary. Even in SLR lenses, a lens marketed at 70mm may not be a true 70mm. With different focal lengths, the area of coverage is different and the meter readings would also be different. However, 2 stops of difference in shutter speeds is a lot, so I would be surprised if it were true.

The P mode or program mode decides on its own the aperture and shutter speed. You can select it to aperture priority mode and at the widest aperture you can get the the maximum shutter speed. Along with that bean bag and/or monopod or even just placing it on the jeep on a jacket as cushion would be of help.
Cheers,
Sabyasachi