I will not go into the technical details explaining the difference between a full frame and smaller sensor like an APC-C sensor format. But it is obvious that the size of the sensor of an average compact camera that the performance of such a smaller sensor will be significantly less. My personal reason why I choose for a full frame is the dimension and the size of the image.
The size of the image of the Nikon DX (crop) format is 4800×3200 and of the FX format is 7360×4912 that means that there is a lot more space if you think you should crop your picture. But cropping your picture has the disadvantage that the quality is going worse, especially if the image is not really sharp as you thought or there is noisier than you want to.
A perfect FX photo 7360×4912 .jpg made with my Nikon d810 Camera with the right sharpness, the correct exposure, with the lowest ISO value could be enlarged to 60 x 70 cm without too many changes on the print it looks even probably the same as on your screen but going bigger the print become worse and the quality will be less.
That’s why the editors of magazines and newspapers acknowledge the importance of having the greatest possible resolution for their pictures before printing. Depending what the photo is used for the higher the resolution the better the print will look.