As I understand it, one of the things that distinguished a Roman army from a barbarian one (or at least a Celtic or Germanic one) was the focus on training and unit cohesion rather than personal glory. Celtic warriors represented the top slice of secular society whereas jobbing Roman soldiers dd not. Swords and other armaments were only really available for the richest.Welllll, it may not be all that straightforward. It *does* seem that the Roman style was more resiliant, not needing to be rigid or on good ground free of obstacles, etc. And 3 feet of space per man (not *between* men) isn't all that great a gap, and no reason to think that a barbarian force would be much tighter. Elbow room is even more important with long spears and swords, axes, etc., than for men with short swords.
As such, individual prowess had a higher cachet amongst barbarian groups. That would tend to count against ordered companies and serried ranks and one is tempted to think more of irregular 'hit and run' tactics of the sort employed much later by the hopelessly outnumbered English army at the battle of Solway Moss in 1542. The English light horsemen (or 'prickers', as they were known) were a scratch force raised from the local border families. They had little or no unit cohesion and would have banded around whichever individual family heads were out with them. Had the enormous Scottish army been drawn in in proper battle array, the English would have lost in about ten minutes, but as it was the English were able to harry the Scottish vanguard as it was trying to form up after getting across the Esk fords. The main part of the Scottish army was stretched out further behind, struggling through the bogs and mires of the Moss itself.
Terrain seems to have been key in medieval battles, presumably because, as at Solway Moss, it could provide a powerful advantage. The English didn't need to engage with the Scots on a long front and slog it out, row facing row. All that had to do was 'prick' (as they called it) - charge, pull back immediately and then charge again. It wasn't about inflicting vast numbers of casualties. It was about causing disarray and confusion. As soon as the English had broken that relatively small part of the Scottish army that had made it over the fords but hadn't properly got itself together, the battle was won.