heavy cavalry engaging heavy cavalry

[Urselius]

The Icelanders also staged stallion fights for entertainment, one is described in Grettir's Saga. The stallion fight led to a grisly-comical encounter, one of the crowd was a beserker who had a grudge against Grettir and picked a fight with him, The berserker, who was mounted, began to work himself up into a frenzy and started gnawing his shield rim - whereupon Grettir calmly kicked the bottom of the shield upwards breaking the berserker's jaw.

The term "line cavalry" implies the standard cavalry of the time, neither of guard status nor having a speciality combat role. In Napoleonic French terms they would be all cavalry not in the Imperial guard or cuirassiers, the status of lancers and hussars would be a bit debatable.