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.
equalizeImage or -equalize
Re: equalizeImage or -equalize
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".