This is another reason for why I prefer The Pacific. The Americans(maybe apart from one character, though not really when you know how it ends for him) aren't really portrayed as heroes. There's even a scene where a large group of American soldiers mentally torture and kill a Japanese solider just for fun.
Band of Brothers is essentially a longer version of Saving Private Ryan, except the premise isn't stupid and the characters are more likeable. Saving Private Ryan has one of the best movie openings ever, though.