Has Jason Bourne been more dangerous to US assets than enemies?

Being a huge fan of the movies, I'll try and answer the question the best that I can.

The Bourne Identity

In the first one, he was in Paris trying to make sense of what happened to him, and out running assassins with Marie. Abbott realized what damage this could have done to the CIA and to a larger extent U.S relations with foreign countries. At certain points Conklin assures Abbott it will be cleaned up, only to fail miserably at each attempt. Abbott kills Conklin, and shuts the program down.

The oversight committee seems to believe Abbott when he says that Treadstone was decommissioned and simply a "game program".

The Bourne Supremacy

The second one sees Bourne in Berlin/Moscow looking for answers as to why the CIA is after him again when he is trying to lead quiet life in India. Abbott was a traitor and wanted Bourne dead simply to stop the investigation of Bourne/stolen money. There is only a brief scene in the CIA, with everyone agreeing that Bourne must be stopped, and they can't have him ripping apart the agency any more.

Unless Neski's daughter confessed to the police, the Russians never find out that Bourne assassinated a Russian politician and his wife because of Conklin/Abbott.

The Bourne Ultimatum

Bourne comes to New York to try and figure out who he is. With the help of Landy, he grabs Blackbriar files and leaks it to the public. At the end Vosen is arrested and we can only assume that the CIA is brought under review.

Jason Bourne

Given that the new movie acknowledges the Snowden leaks, we can assume something similar happened when Bourne leaked Blackbriar. We know one of the assassins was captured and tortured, and blames Bourne for this.

Who received the most damage, the U.S or foreign countries?

It's hard to say because the movies don't focus on international relationships, or what happens after Bourne goes back into hiding. Usually at that point the movie ends. It's more of a personal story with Bourne trying to regain his memory, coming to terms with what he did, and attempting to start over.

We can only speculate as to what happens to international relationships, and the U.S reaction to Bourne. Between the first 3 movies, the CIA manages to keep what there doing under secrecy, because right after Treadstone, Blackbiar happened. Between the 3rd and the 4th is when Bourne does damage to U.S/CIA, but you have to wonder if it has any lasting effects, given that Iron Hand is, to quote Nicky, "worse than before".

Update:

I just checked back and saw the updated part. I'll try my best to answer.

He became internally dangerous at the end of Identity, when he tells Conklin that he no longer wants to do this. Now, they have an assassin with deadly skills no longer under CIA control, and could potentially tell others what he had been though and did. Obviously this wasn't what the CIA wanted but they have to deal with it. I think you can appreciate that the Bourne series while having amazing fight/chase scenes, also works on a level not seen in other thrillers. We see Bourne not wanting to kill out of revenge, both in Supremacy/Ultimatum, he apologized Neski's daughter, and tried to live a normal life with Marie. In a way he became more human, instead of a brain washed 30 million dollar government weapon.