I have the AN on my G11 and use a Gemini on another. It's a hard call to make on which is better. The AN is a great push to, quiet, quick and accurate. You can link it to a planetarium program to show where you are going but it wont "drive" the G11. AN also comes with TPAS for very accurate modelling of your system that will greatly improve pointing accuracy. Accessing database objects with the AN is much simpler and easier I find than using the Gemini hand controller. I also like the silence when using it. No motor noise when you slew by hand
The Gemini will allow you to "drive" from the computer planetarium program. This is a big plus if you need GOTO rather than PUSHTO. It also has modelling abilities for accuracy, but personally I don't feel it is as accurate as TPAS. You can purchase an aftersales product called TPOINT that does the same thing basically as TPAS, but it is an extra. The biggest let down for me with the Gemini is the hand paddle controller. To be honest once you have learnt to use it, it is ok, but I found it a pita to learn the ins and outs of the menus. It is not instinctive and Losmandy would do well to ditch it and use a more conventional hand controller.
They both have pluses and minuses and I guess it depends on how you are going to use it, permanent semiautomated setup (Gemini) or portability (AN), visual (AN), imaging (Gemini). It doesn't mean you cant use either for each, but this is just my experience.