Omaha Beach was tough enough to take without German armor counterattacking. It was critical to keep them off the beaches.
I've seen both movies. The Longest Day was cleaner but I thought it was a much more complete telling of D-Day.
Band of Brothers was also excellent.
Never seen Band of Brothers. Saving Private Ryan gave a better picture of what life was like for a soldier, The Longest Day was, as you said, perhaps a better account of the D-Day invasion.