I personally enjoyed Letters from Iwo Jima more.
Flags of our Fathers is more the story of the famous picture of the raising of the American Flag at Iwo Jima and how it united the war effort, then a typical war-drama. It isn't a conventional war movie because most of the film is shot back in America after the battle at Iwo Jima with flashbacks from the surviving flag-raisers.
Letters from Iwo Jima on the other hand is a classic - the plot is completely linear in this case and focuses on the Battle of Iwo Jima from the perspective of the Japanese army, who were totally outnumbered and facing inevitable defeat, typical Jap-honor style. Ken Watanabe is absolutely brilliant as the Japanese commander.
Take your pick. But like I mentioned already - watch Flags of our Fathers first and Letters from Iwo Jima next. Much better that way.