It all depends on what you are looking for in a marker. The Mini (given that it is a V3) will most likely be more reliable and more efficient. I would assume that they would be about the same in terms of noise and smoothness.
The G3 would be a more comfortable marker. The Mini is, well, mini. You don't have very much room to put your hands. If you have smaller hands this shouldn't be an issue, but if you have bigger hands then you won't have a very good time.
The G3 also has an On/Off ASA, while the Mini does not. It is a great feature to have, but is far from necessary.
Again, it all comes down to what you want out of it. Personally, I would take the Mini if you have smaller hands and don't feel like that would be an issue. However, if you have larger hands, I would take the G3. If I'm going to have a marker, I need to be able to hold it comfortably.
Keep in mind, the Mini is backed by Kee. Kee has great customer service and will take good care of you. People seem to have mixed experiences with Dangerous Power. I personally haven't had any issues with them, but other people have said differently.