First I would comment that if your GIMP processing matches your ImageMagick processing but not the Photoshop processing, the I would have to assume Photoshop is doing something different or extra (such as adding some clipping, IM equivalent would be -contrast-stretch).
Second, the Imagemagick developers do not control Imagick. So we have no knowledge how they implemented that or what changes they might have made.
IMagick is a native PHP extension to create and modify images using the ImageMagick API. ImageMagick Studio LLC did not write nor does it maintain the IMagick extension, however, IMagick users are welcome to discuss the extension here.
I have checked the Imagick "equalizeImage" function at the two different image magick versions and got drastic changes in both the output images. Checked with image magick versions "6.7.8-9" and "6.9.4-10".