The Battle Herald's text actually says as much, so I'm not sure why there's a question:
Issuing an inspiring command is a move action. At 5th level, this becomes a swift action, and at 10th level, it becomes an immediate action. Maintaining an inspiring command is a free action that cannot be disrupted, but its effects end immediately if the battle herald is killed or otherwise prevented from taking actions (such as being dazed, helpless, or stunned). The battle herald cannot have more than one command in effect at a time. She may use this ability for a number of rounds per day equal to 4 + her Charisma modifier, plus 2 additional rounds per level after 1st. She may use rounds of bardic performance to issue inspiring commands, but not vice versa. Inspiring commands are language-dependent, mind-affecting effects. The battle herald cannot maintain an inspiring command and a bardic performance at the same time (this does not preclude abilities such as persistent command or the Lingering Performance feat, which continue an inspiring command or bardic performance after the battle herald stops maintaining it).
The commands state they are normally competence bonuses while performance grants a morale bonus; they're difference bonus types, and the command ability explicitly says you can stack them using Lingering Performance, so I'm not sure how it could be argued that they don't stack...
...with one exception: Inspiring Command can be used to provide the benefits of Inspire Courage, and it says it does so as Inspire Courage, plus it says your levels stack to determine the benefit granted - so my assumption would be that using it for that specific command could not stack with the Inspire Courage. Otherwise that would be sorta gross...