WordPress Thumbnail compression depends on the server?

This depends on two things

  • the image library WP uses
  • the settings of your WP install

Image Library: ImageMagick vs GD

Since WP 3.5 ImageMagick is the default, but if this isn’t available WP will fall back to GD.

ImageMagick generally does have better quality which is why it is preferred.

Settings

There are some filter to change the quality WP uses to resize images, the main one being this one:

add_filter( 'wp_editor_set_quality', 'wpse_176452_custom_image_quality' );
function wpse_176452_custom_image_quality( $quality ) {
    return 96;
}

More details can be found at the announcement I linked to above.


So you need to check if your install differs in any of those factors.