In my view the scene is supposed to show you that Miller's Men are surprised and exhausted. They are either not prepared for such a situation or not willing to make a kill (it appears that the machine gun does most of the killing while everybody else jumped to the ground).
It also shows that the other side is not that much different from Miller's Men. They are in the same situation with the same deck dealt to them.
Additionally, it shows the pressure that they are under when they are in a standoff.
The landing was also a tough scene. But it was a run for the hills with cover fire from ships. It was a different kind of situation and they were lucky to make it off the beach.
Now they are about to catch a breath (Paul Giamatti's Character is even sitting down and fixing his boot) and one second later they are facing down the barrel of a gun.
It is not a video game. If they shoot, will they hit? What if the other person shoots first? Even if it's a hit, will it prevent a counter shot? What about the 20 other soldiers? Will my shot hit the correct opponent or will my allies shoot the same person with 20 rounds leaving all others unscathed?
What if i get hit? Will i die instantly or bleed out? Will i lose an eye or a leg for the rest of my life?
It is much easier to simply drop down the guns. But that only works if both parties are willing to do that.
It is also very similar to animals facing each other. Animals will not try to take a fight they don't have to. There is always a chance to get injured and die because of it. They do not take battles out of joy. They raise their backs and bare their teeth to avoid it. To scare the opponent into retreat or at least a mistake.
Survival is the objective not extermination of the others.