It depends on style. What kind of rules does your group like? What are they more focused on- action/combat, espionage/intrigue, drama, story?
Shadowrun 4e is solid and has the potential for GitS style drama. AI, Full conversion cyborgs (you would need to just give that out in char gen, I don't think a starting character could afford it), genetic experiments, corporate greed. The setting could support a GitS-style game, but I wouldn't try "porting" it over. I think if you focused your Shadowrun missions on the tech vs. humanity drama, you could easily invoke the moods and themes in GitS.
Cyberpunk 2020 could also accomplish this and there are conversions out there for the actual universe. There is a new fan-created version of Interlock (the system in CP2020) called Interlock Unlimited. And it's free! It still has a solid fan base. Also, that gentlemen (known as Wisdom000) also did some online conversion stuff for various Anime to Interlock including GitS IIRC. He is a great fan of the game and he ran playtests and online groups to vet the updates to the system.
Now, for a less rules intense game, I would recommend you check out PDQ by Atomic Sock Monkey Press. This game is really hitting my happy buttons right now. It is a more story-focused ruleset and I think would make for a perfect GitS-Style game. You can download the PDQ (and the newer PDQ#) rules from the ASMP website for free!
Also, FATE 3.0 as found in Starblazer Adventures is another great story-focused rules-set. It's actually a tad crunchier than PDQ and has plenty of options to pull off all kinds of sci-fi gaming. Worth checking out. I just got my hard cover from my pre-order and it's one awesomely huge book (also fun to read btw)!
Actually as I think more about how PDQ and FATE handle cinematic action, mooks, and the like, they would make a really good fit. The main characters can do awesome stuff AND survive plenty of punishment while mooks are mowed down like flowers...
In the future, I think I am moving away from more traditional style medium/heavy crunch games to lighter more story-focused games. These last 2 games support more player-centric gaming, player control over plot and scenes, encourage roleplaying both the bad stuff as well as the heroic, and get the game focused back on that collaborative story creation that I want. I have grown tired of arguing about range modifiers and subsystems. I want drama and adventure!
If I was to run a Cyberpunk GitS style game, I personally would try either PDQ or SBA.