When I said "disadvantages" I did not mean in the technical aspect of cavalry and such, since those were negated by Harold's strong defensive position. But the exhaustion counts as more of a disadvantage as it would seem since, from my experience in organizational work, exhausted men get crankier and more recalcitrant and less likely to obey orders--and more eager to get everything over with, and that might partly explain their impetuosity in the pursuit of the Bretons. The exhaustion alone would have been enough to undermine much of the advantage Harold had in terms of cohesion.

And of course, even though William's army might have been more heterogeneous, the core of his Norman reserves under his personal command would still have been a fairly unified body capable of responding to changes in the battlefield situation. That was the actual point about the Norman veterans and all. Harold also probably labored under the restriction of keeping his troops in formation--which meant that his reserve couldn't operate in as mobile a manner as William's if he didn't want to risk his troops mistaking the cues and leaving the defensive positions to follow them.