Appleseed (Movie)

They both have similar animation, futuristic setting, a female main character, and both have androids (robots, bio-bots etc).  

Both movies have the marvelous mind of the sci-fi guru Shirow Masamune behind it, so you must expect a good storyline (Appleseed's not a masterpiece as GITS, but it's interesting anyway). The animation is awesome too, and the action scenes will keep your eyes on the screen until the very end. If you're a sci-fi fan, both movies are a good shot. 

they are both about police using robots to fight crime in the future 

The underlying themes are similar. A global system that totally controls behavior of individuals in a futuristic town depicted in a quite elaborate sci-fi fashion. An attempt to dissect the eternal dilemma of happiness vs free will. A happiness that is nurtured/enforced by the system in order to prevent the basic barbaric instincts of human race from instigating suicidal wars.   Pacing-wise, the two movies start off with a cool action sequence involving the heroine and while Harmony becomes a somewhat philosophical contemplation woven around an investigation by a Helix inspector (the heroine) Appleseed keeps being more action-packed. 

Police after criminals in both have main character girl and said character gay , helping him his life and partner.  

police forces on the street, futuristic cities and in some cases half cyborg villians run on the loose, Both have same job they´re cut out for and have a man&female main cast with the right TO BEAR ARMS!! phew 

Both movies are full of action, cyberpunk, sci-fi weapons and gadgets, with a few high-quality hand-to-hand combat scenes, both have a female protagonist and what left of civilization is controlled by an artificial intelligence system that decides what is best for people, but the methods are questionable and those questions are raised by the female protagonist in her dangerous journey. 

Both have similar CG, and both deal with the idea of a utopia.  

Appleseed and The Spirits Within are sci-fi movies done exclusively with computer generated technology, which lends them the same overall feeling, 3D animation dominating the viewing experience almost completely. The plot is similar, in both cases humanity is at the brink of extinction and it is up to scientists to come up with solutions.  

Both have high amounts of action with mechs. Even though IGPX is a very short arena battle type series the mechs seem quite similar.. 

2B (Nier) and Deunan (Appleseed) are soldiers in a post-apocalyptic world ruined by a devastating war that has decimated the human population. The main characters are embroiled in a conflict that will determine the fate of humanity and the rise or survival of artificial life (e.g., bioroids, robots). Appleseed has dated 3DCGI, but you know whether this is a problem like every old anime. The ethical dilemma and philosophical discussions are very much central to the plot in Appleseed. Nier has a more subtle approach. Sci-fi is at its best when it explores important themes. If you agree with this statement then you might enjoy this recommendation. read more 

They both rely heavily on CG but the work is exquisite. The stories are also in similar settings, the desolate future. If you liked the animation style and storyline of Appleseed then you may want to try out Wonderful Days.  

Another cg movie. Appleseed has more story, but main similarity is the full cg they both share.