Commodores are usually the highest rank to fight in the front lines, so they are trusted to make careful decisions. There always is one Commodore per fleet, unless it is carrying multiple companies with different objetives, (Otherwise the companies will be joined under one Commodore) and he or she is in charge of making all important decisions. This is to prevent arguing over who is in command.
On the ground, they are allowed to take any position in their unit, from covering them with a sniper rifle to leading the charge in a tank, or with nothing but a sword. Commodores are usually equiped with medium armor and point defense gauntlets, but can use whatever they want.
In space, Commodores will command their ships, but often pefer to lead boarding parties or defend from hostile ones.