If I travel from Hungary to Serbia, I have already passed the Hunagrian border control and then get involved in a road accident before entering Serbia (in the zone between the borders). Is this neutral territory? Should I call the Hungarian or the Serbian police?
Without any relevant exception I can think of, there is no such thing as an "area between land borders". A land border between two countries follow in almost all cases a very well defined path and what you actually mean is the area between two border control posts.
If you e.g. locate the border crossing on E75 between Hungary and Serbia on Google Maps, you can see that the actual border is pretty much exactly in the middle between the checkpoints.
So, even if you travel from Hungary to Serbia on this road, have passed the Hungarian checkpoint and for immigration purposes technically left Hungary, you are still in Hungary until you cross the border.
In many places the area between the two sets of border guards is taken very seriously indeed and is under the control (the firm control) of one of both sets of guards.
Since the natural reaction to a car accident or even a stalled car is to get out, either to look at the damage or to talk to the other driver, do this first, with caution.
There is a good chance that someone will yell loudly at you not to get out of the car. Friends of mine had a car stall in the 10m or so between the US and Canada border, tried to get out to push it, and honestly thought they were going to be shot. By Canadians. Border zones are serious. If this happens to you, freeze. Optionally, get back in the car. Someone will approach you. Report the accident to that person and do what that person says.
If nothing particularly happens when you get out to do the usual car trouble things, feel free to call the police force of your choice and report the accident. Should there be some administrative reason why you need to call the other police force, or the border authorities, the worst that will happen is you need to make a second phone call.