I was recently having a discussion with a statist and opened their eyes to the idea of panarchy. When I told her how she could have her government that takes from its members and gives it to other members while I have another form of government that upholds the ideas of life, liberty, and property, she asked me a question I wasn't prepared for at the time. Her question was, how would crimes involving two different subjects work?
I wish I would have had a brain storm at that moment but hindsight is always fifty-fifty. Afterward I gave it some thought, and I realized the answer is in our reality already. What happens when a member of one nation-state(America) commits a crime against another member of another nation-state(Canada)? The rules between both example nations are similar, or at the very least have similar priniciples.
Before we begin, this is all theory, since we today don't have panarchy, and is more or less a mental exercise to show that non-territorial governments along side each other can work.
My government and hers, for example, both might hold life, liberty, and property in high regard, such as American and Canada. What defines life, liberty, and property, may be different, the history of both is different. Today when two nation-states have an issue with each other they send members to try to hash it out and fix whatever the problem is. So under panarchy, or non-territorial governments, so too would they send members to hash things out, the only alternative is violence, which is unacceptable.
Governments who have members sharing the game geographical area would most likely have 'treaties' between each other, which might dictate how they solve problems between each other. Of course two differing ideological based governments, might not be able hash things out. In that case, one solution would be to try the case in both government's courts, with the defendant having to serve out both sentences in order to maintain good standing in both governments.
What happens with the sentence is diametrically opposed to each other, such as a penalty of death? You have to remember that you have the choice of which government to choose from, just as you do with religion. It is because of this option, that people will tend to go with governments that have ideals that most people believe in. This creates a open-market on everything, including justice, an as such, most governments, as they currently do, do not have death penalties, so you most likely wouldn't see any government turning to death as a punishment. Of course this doesn't answer the question, does it?
If two governments had two different punishments for the same crime, you'd most likely see the government with the most reasonable punishment having more people, and therefore those with less people would find themselves soon out of the government business.
Currently people who are convicted of 'serious' and 'non-serious' crimes are put in cages, however this punishment for both the criminal and the victim, where in the victim has to pay for the criminal to be in jail as well as the original crime. Putting people in cages doesn't appear to work very well, look at the number of people in prisons world wide, and then look to the rates of recidivism. Granted some of the recidivism rate can be blamed on a number of other factors, such as the difficulty of ex-cons obtaining good paying jobs, the profits of illegal activities, and many others, however if putting people in cages worked, then why is the rate so high?
To the point that if two governments had two different punishments for the same crime, the guilty would have two sentences to serve, providing that the guilty wish to maintain relationships with people in those governments. I have no doubt that during business with people who haven't served their sentence would have some type of negative effect on those who choose to do so. More totalitarian governments might make it a severe crime to do business with them, however more life, liberty, property governments might resort to ostracization as a method of getting people to 'do the right thing'.
So basically put, the answer to how would two non-territorial governments, using an panarchy method, would solve problems between different subjects similarly that current territorial governments do, through negotiation and talking out the problems.