See budapest story is the main plot of black widdow movie. So it will be revealed in black widdow movie

It will be clear in the upcoming Black Widow movie.
Though whatever happened, Clint and nat were probably on different sides (as Clint mentions that they both remember Budapest differently)

Budapest is the main plot around which the next movie of MCU’s Balck widow is based on.

To know what happens in the Budapest we have to defenitly wait till the black widow movie shows up as the entire movie revolves around it

Budapest has affected them mentally and for good,of course,but in particular this scene shows how close they became in there