Although I don't know the specifics of those cameras, first you have to take into account sensor size. For the same focal length different sensor size will yield a different field of view. So one solution is to determine the crop factor for each camera and set the zooms at the same 35 mm equivalent focal length. This may be difficult because I suppose that on those camera you don't have the option to set the zoom at a specific focal length. Another solution is to place or select markers in your scene that delimit the field of view and by making test shots set the zooms so you'll have the same field of view.
Another problem is the depth of field and, according to the specific situation there may be a difference due to different sensor sizes. This may be corrected, if necessary ( compacts have a generous DOF) you'll have to adjust differently the apertures in order to have the same DoF. this Leeds us to the exposure part, it has to be the same, but I suppose that those cameras shoot only JPEGS and in camera processing is different from brand to brand. you'll have to do test shots with each camera in order to find settings ( contrast, saturation, sharpening, white balance- this one is better if it's made with a grey card for both cameras -and so on) that give you almost the same results.
Hope that helps.
Oh one more thing, if there is a difference in sensor picsel counts you may have to resize the pictures in post production in order to have the same dimensions.
Canon PowerShot S100
Canon 50D , SIGMA 10-20 f3.5 ,Canon EF 24-105 L IS USM, Canon EF 100/2.8 macro Canon EF 50/1.4 ,Canon EF 85 f1.8,Canon EF-S17-85 4-5.6 Old Tamron 28-300 inherited from my Canon Rebel G film camera