Band of Brothers is arguably the very best WWII ground combat re-enactment ever produced, especially as it is based closely on real life exploits. The realism, as I can best equate from studies and discussions from those that were there, is spot on. Notice who produced it and who was involved in Saving Private Ryan. That should tell you something.
Flags of Our Fathers comes close to the same level of realism in the combat scenes and is overall very well done. But the movie style is, as said before, a bit too jumpy in it's flashbacks. It will be 15 to 20 minutes into the movie before you get to understand the flow, plot and real focus of it.
I as the topic was of great interest I easily stuck it out until I got into the sense of it. One important note, it is very, very historically accurate on most every point I can determine. Who died, when, and how. The homefront scenario, the finacial crisis, etc., was all true to life. The biggest thing I got from the movie, which I knew intellectually, but the movie really brought home, is just how close we came to losing the war due to financial and economic exhaustion. I believe this is a rarily acknowledged contributing reason for the authorization to drop the A bombs on Japan and get the war over quick.
Definitely, worth seeing and having any of these productions.