So far from home, I'd think it depends on the agents and situations involved. Most are probably going to ignore each other-- why add to your list of enemies needlessly? In Krakow, for instance, I think they were beginning to take on a non-hostile relationship. Both are going to be very cautious, afraid of not only getting sucked into the other's control, but of making it easier for the KGB to roll up both their networks at once.
In general, the CIA fellows are going to have to be a lot more sneaky, as they have effectively zero chance of getting help from any US military assets nearby. They're going to have to lean a lot more on locally-recruited folks, like their 10th Guards Tank Division outside Warsaw.
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My Twilight claim to fame: I ran "Allegheny Uprising" at Allegheny College, spring of 1988.
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