Beowulf brings fourteen of his best Geats with him to fight Grendel. One is sacrificed before the battle of Grendel. The thirteen who remain are loyal and eager to help their lord. When he descends into the lake where Gredel's mother resides, they ring the perimeter of the lake, along with Hrothgar and his men, and wait for their lord to return triumphant. After killing Grendel's mother and removing the head of Grendel, for a trophy, the lake's surface becomes clotted with blood. The men who await Beowulf fear he is dead and will not return. Hrothgar and his men leave the scene and return to Herot for a meal. Beowulf's men remain out of loyalty and have only a semblance of hope that their leader will return. When Beowulf fights the dragon, he is a much older man, and has ruled Geatland for fifty years. He is determined to rid his land of the dragon and still seeks fame and glory. Beowulf again selects the bravest of his warriors and tells them to wait for him, in case they are needed. He will fight the dragon alone, if possible. The dragon is a fearsome adversary. Its flames melt Beowulf's shield, and its hard skin is responsible for his sword breaking. Fire engulfs Beowulf, and his men, rather than help their leader, run into the forest and are afraid. The difference one sees when comparing the two battles is the reaction of the men. In the fight with Grendel's mother, Beowulf's men do not leave. In neither instance do they fight, but in the battle with the dragon they let down their leader and appear cowardly.
In the anonymous Beowulf, the epic Anglo-Saxon poem, the comparison between Beowulf's followers' involvement in his fight with Grendel's mother and with the dragon is easy and simple: they're not involved; at least not much.
No one else is present when Beowulf fights Grendel's mother. He is alone in her den.
When Beowulf fights the dragon, his followers run away, so they're not involved in that fight either. The only exception is Wiglaf. He stays and helps Beowulf fight and eventually kill the dragon. He is a loyal and brave follower of Beowulf, but he is the only one.