In this comparison I was interested in the differences when using the APS-C 55-300mm lens on the KP vs. the full frame K-1 II.  The first image shows the result when using the lens on the K-1 in FF mode at a true 300mm focal length.  You can see the vignetting, but I planned on cropping it out since I am only interested in zooming in closer when I use this lens.  The second image is from the same lens on the APS-C KP camera at the 300mm setting which is an effective 450mm on this camera. 

There is a difference in the image quality between the K-1 and the KP cameras.  The K-1 image, the first one is more pleasing, but in this case I think the KP is the better camera to use the 55-300mm lens on since I am interested in getting “closer” and it gives me an effective 450mm focal length.  It is harder to compare image quality since there is a difference in the ISO, aperture, and shutter speed chosen by each camera in their program modes.  In addition, the difference between the number of pixels is not sufficient to warrant cropping the K-1.  If I were to use the K-1 in the crop mode the compositions would be closer to the same on both cameras, but the K-1 would have far fewer pixels available for cropping.

The images below were made with the FF K-1 using the 55-300mm lens at 300mm when photographing through a window.  The bottom line is that I can make the lens work on either camera but that if I’m planning on capturing a distant view, I would probably use the lens on the KP camera.