Koukaku Kidoutai: Stand Alone Complex - Solid State Society

Both made by Production I.G., both have mostly cyberpunk elements, but the most interesting thing is ending of GitS SSS, where Motoko says 'maybe a new society that we have never even dreamed of is already being born', and about 70 years later in Psycho Pass, we have new society determined and controlled by 'perfect' Sybil System. I see very interesting connection here, and i am pretty sure that Psycho Pass creators were inspired by GitS Stand Alone Complex universe. 

Similar cyberpunk settings and concepts. Ghost in the Shell tends to be more philosophical while Vexille is more action oriented. 

Dual Matrix is nowhere near as good as SAC - SSS, but it is similar in that it's a follow-on to a sci-fi series that is cyberpunk to a greater or lesser degree, and features an almost completely cybernetic female lead and her part-cybernetic, part-human male partner. Also, both can be taken as a single unit, in that you can watch them if you've not seen the series they follow; however in both cases it's advisable to watch the series, just to get more of a good thing, and arguably a more satisfying overall story.