In this film Burgoyne is skittish and worried, rebuffs an officer about risking his men's lives using bayonet charges. In fact, Burgoyne was the leading proponent of the bayonet, even issuing an order that the soldiers were not allowed to fire their weapons without a direct order and that the supremacy of the British bayonet was to be impressed upon them. He'd had experience fighting the Spanish in an earlier war and was not a reluctant warrior.
Also in the movie he's a bit timid because he states the rebels have them outnumbered by six to one. They were in fact outnumbered (probably more like four to one, although accounts from the time vary) but he did not know it because his Indian scouts had deserted after Bennington and he had trouble getting intelligence reports. In fact, he led the last battle as a reconnaissance mission to test the enemy's strength, and had promised his subordinate generals that he'd (finally) give in to their pleas to retreat if the enemy was too strong. That recon mission proved to be his final reckoning in the war.
But watch the movie anyway. It's very entertaining.