It turns out that the images on the OPUS website have been processed and calibrated to produce 8-bit images with the minimum intensity in each image set to 0 and the maximum intensity to 255. (The original raw Lorri images have 12-bit light level values which are converted to 32-bit double-precision numbers by a ground-based calibration.) Every web image may have a different dynamic range and scale.
The raw and calibrated images in Flexible Image Transport System (FITS) format can, however, be downloaded from the OPUS site. (Just click on the links above, add the image to your cart, then choose the formats you want to download.) It is not possible to upload .fits images here, so I have converted the top two raw images (lor_0408486979_0x633_eng.fit and lor_0408486989_0x633_eng.fit) above to png and show them here:
The two images are very similar, with the major difference being the short horizontal line in left image's upper right quadrant, that is almost certainly a cosmic ray. Raw LORRI images typically contain a few cosmic ray strikes which can appear as bright pixels or short streak. Such bright streaks can significantly change the light intensity scale, making dimmer stars invisible in the web images, which is likely why many fewer star are visible in left web image in the question. I would guess than even tiny changes in pointing the camera could also cause the scale in the web images to change as the brightest star may be spread over different numbers of pixels, changing the intensity of the brightest pixel.