Anyway, using a different library than libjpeg would not change much: Photoshop cannot use a better (or worse) algorithm, because the JPEG compression algorithm is standardized and has to be implemented in the specific way if you want the files to be readable by any JPEG viewer.

The differences that can be observed between both programs are not related to the algorithm, but to the quantization tables that are used for the JPEG compression. These tables define how much of the original image is kept when saving (specifically, the divisors in these tables influence how many DCT coefficients are kept). Each table contains 64 numbers and is included directly in the JPEG file because it is needed for decompressing the file later. There are usually 2 or 3 quantization tables in the file: one for luminance and one or two for chrominance.

When you select a given “quality level” in GIMP (libjpeg) or in Photoshop, you are asking the program to generate the quantization tables that have been associated with that quality level by its developers. Different programs use different tables, but they usually have many similarities. That’s why I created the tables included in this article: they allow you to find the quantization tables that are similar in both programs.

Considering how JPEG compression works, I would be very surprised if you could find some images that produce better results in Photoshop than in GIMP. What happens is usually the opposite: GIMP saves JPEG files that are smaller than with Photoshop but have the same (or better) quality. One of the simple reasons for that difference is that Photoshop includes more metadata by default.

Is it because Photoshop uses a better algorithm? Perhaps there are any alternatives to libjpeg which can give a better size/quality ratio?