Vince has it right, it is a designers choice. Depends on the application.
Moving the mass away from the center point of rotation will increases the moment of inertia. Which means it will resist influences from external forces more.
This includes both environmental disturbances and self generated motion command updates. One of these is not wanted, and the other is wanted. This leaves us with the trade off in design decision. What you choose will be application specific.
If you choose to have a responsive craft that is quick an aerobatic, it will come at the cost of the controller continuously fighting external disturbances. There will be a limit to how fast it can respond (bandwidth), and consequently will be more unstable given large, or rapidly varying disturbances.
Conversely, if you want inherent open loop stability, it will come at the cost your craft being slow to implement it's own desired motion updates.
I am doing my first build at the moment. I want to start with high controller bandwidth given the mountain environment I am in. My current conundrum is, do I put the battery on top or below. I really want it below.
Primarily because I am going to be changing things up down there when I start adding peripheral components to interact with the environment. It makes sense to wire up the computer with all fixed parts on top and then it's done, permanently.
But this does leave me with two issues. One doesn't want to get into the inconsistent delayed response that yoos brought up that will occur when something is dangling on a string. I can synch up the battery but it is quite a bit of effort each time for both axis'. Maybe I just need to invest in a better battery strap than my 1 dollar Chinese Velcro.
The real thing bothering me right now is risk, the idea of an unstable battery being exposed. I've got the heli-style Tarrot landing gear, and in a big fall I don't see it doing much to protect the battery.
So my question to expand this discussion here is: What are people doing in terms of top or bottom? I like the idea of it being up above, but that leads to numerous different awkward other placement problems down the road.