The f-stop thing depends on what you're doing.
If you are in the same place, taking a picture with FF and crop, the crop will appear to have a longer focal length. Since the sensor is denser, you'll blur sooner at the pixel level. Since you're looking at a smaller part of the image, you'll see more overall blur, as the blur appears magnified just as much as the in-focus parts.
If the crop image is taken from further away, in order to maintain the same framing as the FF image, the results change. The increased distance results in less blur compared to the FF image, as though you were using a smaller aperture.