The reason we see such battle traits in these two people is that they both belonged to a tribal organisation, whose head was typically a warrior figure. The ancient Germans who went volkerwunderung possessed both an individualistic fighting spirit and a collective form of fighting organisation. The Germans recorded by Tacitus were not so well organised, but hundreds of years of contact with the Romans had changed that. By the time of the fall of West Rome, Germanic and Gallic soldiers were proficient group fighters. Individualism no longer quite cut it.
Ultimately, chivalry was a military ideology which emerged in the midst of a feudal society with poor central government power that was exposed to continuous and unpredictable outside attack. Chivalry was a product of the society and environment it emerged in, rather than a continuation of a form of battle fervour that had been abandoned in favour of better organisation hundreds of years previously.