essentially they first hired baldwin, who was not a leading man but had already done some big movies, and it was going to be more of a traditional vehicle for baldwin.
then they hired sean connery, a genuine movie star, and he wanted them to expand on his character and make the soviets more interesting and human as a result. they had too or wanted to take advantage of connery's star power and the result is a much better story.
i read rainbow six because i played the game, and while i enjoyed it, even me as a 13 year old boy was kind of disturbed by how 20% of the book is lurid descriptions of the beauty and efficiency of our weapons. long descriptions of how the troopers are super competent, long descriptions of the precision and mastery of the snipers, how the guns are well oiled and wonderful tools, etc. real psycho stuff. also the bad guys are environmentalists planning to kill everyone on the planet with a engineered virus lol