Wordpress Thumbnail compression depends on the server?

Different image weights were generated in different servers when Uploading images to Media.

For instance, an original image of 2.1Mb uploaded to a server generated a 700Kb image, for the medium size, which is too big. The same image uploaded to my local server, generated a 70Kb image for the medium size, which looks horrible.

Does anyone know what it may be due to? What parameters affect the image compression rate?