One image is 15mm, the other between 28 and 70 mm. The bigger image (esp the bigger background) is probably the longer lens.
Crop and full frame is not about detail. It is about frame area.. (and while it depends on the sensors, also possibly about the size and numbers of the pixels in that area)
If using the same lens on both, the image out of the lens is the same of course. Digital merely tries to reproduce it.
If using the same lens on both, and standing at same spot, full frame shows the scene half again wider (not cropped smaller).
If using the same lens, cropped DX has to stand back half again farther to show the same scene in the smaller area (so we use shorter lenses - then depth of field changes when we stand closer - however DX generally has greater DOF).
All of the images are presented on the number of pixels that the sensor can do (which varies in models). Digital noise and high ISO performance is improved by pixel size, which depends on pixel density in that area. And the (lens image captured by the sensor area) DX image has to be enlarged half again more for us to view it the same size later.
See
FX - DX Lens Crop Factor