First, a lot of setup
For this answer I have to make a lot of assumptions about how AI's work vs. how organic brains work. I find the most meaningful answer coming from a quad chart based on two ways of valuing a "thing." They're certainly not the only two ways to value things, but they prove useful for me when thinking about AI.
I chart value of objects on how well an object behaves when it works "as defined," and how well an object behaves when it works "out of spec," (i.e. when you ask it to do something you don't think it's "expected" to do, how well does it keep up)
Out of Spec Behavior
Poor | Good
As Good | Tool | Interesting |
Behavior Poor | Crude | Resilient |
- Crude things are not good at anything. They fall apart with use, and are generally not very good at adapting to new situations. The modern human category of "child's toys" fits in this block.
- Tools are amazingly good at what they do best. Once we devise a tool, and understand its abilities, they prove amazingly good at accomplishing goals. However, they are often very narrowly focused, unable to adapt to changing environments. A helicopter can fly in ways that are a marvel to behold, as long as they are kept within spec. However, on Everest, humans climb higher than any helicopter can go because the air is too thin. There was a famous rescue on the lower slopes of Everest where a helicopter pilot decided it was worth the risk, but refused to land at that altitude for fear the machine would not be able to take off again. He instead hovered just a few feet off the snow, carefully feeling for a sign that the helicopter was leaving its spec range.
- Resilient objects just keep working, against all odds. Some systems are not known for their ability to perform in ideal conditions, but in unpredictable dangerous environments where one does not get to prepare. Survival gear tends to fall in this category. As one example, there is a military technique nicknamed "dummy cording" where you discard the core out of some parachute cord (to save weight) and use the outer sheaths to tie your gear to yourself so that it stays around in times of great exhaustion. Parachute cord was never designed for this operation, but its construction is so resilient that it turns out to be useful, even after you've taken the strong part out.
- Interesting objects keep our attention with their behavior. When we try to use them "in spec" as tools, they function perfectly, beating our wildest expectations. When we have to use them "out of spec," they keep surprising us by never failing, even when submitted to environmental conditions far outside of their "operating environment." Military equipment often fits in this category. Consider the famous pictures of helicopter halos in the desert from sand hitting the rotors, or the A-10's legendary ability to fly, even after taking hundreds of rounds. Even those who understand the physics of what is happening and the design decisions that lead to it are awed by it at first sight.
All four of these categories are relative to the observer. A Swiss watchmaker would draw the boundaries differently than an Amazon tribal elder would.
I put forth an (unproven) hypothesis that AI's and organic brains take a different path through this quad chart.
If you believe in evolution, Organic Life consists of all of the really good random discoveries genetics found over millions of years. Along the way, each of these ideas are subjected to a remarkable number of varying scenarios. The ones that survive are ones which improve survivability, but more importantly are versatile enough to be useful in thousands of unexpected situations. Organic life improves itself by trying to go from Crude to Resilient to Interesting.
AIs are generally computer programs. Programs were originally tools. Currently our programmers are very good at making computers do astonishing things in spec, but we are not very good at making the computers do good things when we surprise the printer. This is the source of great frustration for any IT person who has to explain why the user's input wasn't "spec," so the computer is failing. AI seeks to be more and more versatile, handling situations the programmer did not think of. AI improves itself by trying to go from Crude to Tool to Interesting.
As an over-generalization, I will assume your biological and AI centric human civilizations will continue to develop along these general principles.
The most obvious effect of these two paths is that the AI centric civilization will want to change its environment more drastically than the biological based one will. This is because a intermediate grade AI is a Tool, which means it works well when you can apply it "in spec." The easiest way to make sure these Tools function is to change the face of the world so that it is easier for a user of the AI Tool to be confident that its use is "in spec."
Biological based civilizations will be less inclined to change their environment. In fact, if the environment is complicated and hostile, it makes it easier to ensure all of its creations are Resilient. Your biological civilization will be fine with a world where they can never tell if their creations are operating "in spec," because that isn't as important to their civilization. They would easily create amazing creations, but their amazingness would show up in the resiliency of their designs. You wouldn't see a bio-jetpack that can be used once to assault an AI tower through an unprotected ledge, but you might see a jetpack that can be used continuously, and has uses for fanning the eggs of young creatures in hot summers. This isn't because the giant brains can't figure out how to make such a one-shot device, but rather because the giant brains wont want to make such a device. They've been raised to look for more resilient solutions.
Now for the mixing and the war
We will assume each side has a strong cultural identity: they believe their approach is superior enough to distinguish "us" from "them."
From the biological perspective, there will be only one possible response to mixing: increase the complexity of the environment. If they are fearful of the AIs, then they will seek to make "them" unable to progress. A complicated environment means it's harder to tell that Tools are operating "in spec," limiting AI's ability to leverage all of its creations. On the other hand, if they seek to coexist with the AIs, the they need a way to make the AI's robust like their culture. To do this, they would wrap the AIs in environments that are designed to appear simple to the AIs (letting them use their tools), but on the outside, such environments are highly resilient (so the Biological can make sure their friendly AIs never face complicated out-of-spec environments).
From the AI perspective, there is also only one possible response to the mixing: simplify the complexity of the environment. If they are fearful of the Biologicals, then they will seek to achieve a strategic advantage by paving over all of the complexities of the Biological environment. If they seek to coexist with the Biologicals, then they will need to develop a common ground where they can safely interact with Biology without fear of going out of spec.
So from both perspectives, there is a natural desire to segregate. The most Interesting AIs will seek out the most predictable regions far away from the Biologicals, to make sure they are never driven "out of spec." The most Interesting Biological creatures will seek out the deepest most complex natural regions of their area, far away from the AIs, to make sure that any dangerous Tools are blunted by the journey to their home.
The middle will be colonized by a mix of Tools and Resilient creatures which have to seek out their own living after the most Interesting creatures take the prime real estate. The more you want to minimize the mixing, the more you need the young Tools to look up to the intelegence of their Interesting AI masters, and the more you need the young Resilient creatures to look up to the wisdom of their Interesting organic elders. It would be up to you as an author to decide how far you want to take that.
However, consider that such mixing may not be such a bad thing. Consider that your average adult cannot compete with the wisdom of an elder. Consider that your average sword cannot compete with the awesome capabilities of a firearm. But give an average adult a sword, and put it in a realm with wise-but-unarmed elders, and firearm wielding-but-mindless drones on the other side, and suddenly they just might be able to hold their own.
And darn shame if after millennia of conflict over who the rightful heirs to humanity are, if a group of humans which are viewed as Crude by both AI and Biological masters alike can suddenly stand in the middle of these two great forces and proclaim them heirs to both of their lineages.
Balancing the Game
Very often we assume that AI's will naturally win over Biology, but there's some argument for why that isn't naturally so. AI's are better at solving small, well defined problems. Biology is better at solving vague large problems. Consider the health of an ant colony. If we want to kill an ant colony, its not hard. We put some ant-killer down, let them eat it, and laugh in our superiority.
The ants laugh too. By biomass, they outweigh all humans together and are found on nearly every type of terrain on this planet. The ants are far less concerned with the loss of one colony. Maybe they are winning?
Interaction between AI and Biology would consist strongly of the AI side striking for a small well defined goal with a superior force, and capturing it virtually every time. However, the Biologicals would seek to make it a Phyric victory. They want the AIs to win the battles but lose the war. Their tactics would involve letting the AIs get what they want, but making sure that in each battle, they give more than they capture. Biologicals would excel at giving up a township, and using that to misplace the AI armies and sac an AI city in trade.
The AIs would try to predict their behavior, and that's where the real balance would lie. Biology is highly chaotic. It is virtually impossible to predict what a mind will think of next. Chaos is the enemy of AI planning. You can't apply logic to it, because the purpose of moving chaotically is that it is impossible to tell if an attack is going to be a minor skirmish or a major war. Not even the Biologists would know which it would be, until the last moment. That's where the Biologists can return the balance to even.
There is a fighting style where you set up your self and your environment such that you don't prevent your opponent from doing anything, and you don't commit to anything. You just make sure that you get a slight advantage no matter what they do. Then you wait. Due to a lot of math I wont put here, I've found this is much easier to accomplish with Biology (focusing on Resilience) than it is to accomplish with AI (focusing on logic and Tools). Biology would give the AI a few billion options, all of which look good, but each of which is flawed. The AI would have to analyze each of them, while the Biology knows that it doesn't need to. Whatever path the AI chooses, Biology is ready.
This technique is very dependent on chaotic behavior. If the AI chooses to do nothing, then their predictions become exponentially less accurate, which is brutal for long term planning. This technique forces the AI to make a choice, without giving it time to make the choice wisely.