The quality you see depend of the resolution of your original HDRI, the larger (pixels) the image the more resolution 'sharper' it will look.
Having a very sharp HDRI to be used as illumination is not optimal because it create 'fireflies' in your render image.
If you would like to have a sharper image as a background, you should follow tutorials called IBL workflow.
Or change the background in Photoshop.
