Who "won" in the battle of Red Bank? The Americans or the British?

BATTLE OF RED-BANK.
THE British army had been successful in repulsing the Americans, yet their situation was not comfortable; nor could they easily maintain themselves in Pennsylvania unless the navigation of the Delaware were opened, and a free communication established between the fleet and army. The upper line of chevaux-de-frise was protected by a work named Fort Mifflin, erected on a marshy island in the Delaware, called Mud Island, formed by an accumulation of sand and vegetable mould near the Pennsylvania bank of the river, and by a redoubt called Red-Bank, on the Jersey side. At a small distance below Mud Island, and nearly in a line with it, are two others, named Province and Hog's Islands; between these and the Pennsylvania bank of the river was a narrow channel, of sufficient depth to admit ships of moderate draught of water. The reduction of Forts Mifflin and Red-Bank, and the opening of the Delaware, were of essential importance to the British army in the occupation of Philadelphia. In order, therefore, that he might be able more conveniently to assist in those operations, General Howe, on the 19th of October, withdrew his army from Germantown and encamped in the vicinity of Philadelphia.
He despatched Colonel Count Donop, a German officer, with three battalions of Hessian grenadiers, the regiment of Mirbach, and some light infantry, to reduce Red-Bank. This detachment crossed the Delaware at Philadelphia on the evening of the 21st of October, and next afternoon reached the place of Its destination. Count Donop summoned the fort to surrender; but Colonel Christopher Greene,of Rhode Island, w lio commanded in the redoubt, answered that he would defend his post to the last extremity. Count Donop immediately led his troops to the assault, advancing under a close fire from the fort, and from the American vessels-of-war and floating batteries on the river; he forced an extensive and unfinished outwork, but could make no impression on the redoubt. The count was mortally wounded; the second in command also was disabled; and, after a desperate conflict and severe loss, the assailants were, compelled to retreat under a fire similar to that which had met them in their advance. Colonel Donop was made prisoner, and soon died of his wounds.

The disaster did not terminate here. That part of the fleet which co-operated in the attack was equally unfortunate. The Augusta, Roebuck, Liverpool, Pearl, and Merlin, vessels-of-war, had passed through an opening in the lower line of chevaux-de-frise; and on the commencement of Count Donop's attack, moved up the river with the flowing tide. But the artificial obstructions had altered the course of the channel, and raised sand-banks where none existed before. Hence the Augusta and Merlin grounded a little below the second row of chevaux-de-frise. At the return of the tide every exertion was made to get them off, but in vain. In the morning the Americans, perceiving their condition, began to fire upon them, and sent fireships against them. The Augusta caught fire; and, the flames spreading rapidly, it was with the utmost difficulty that the crew were got out of her. The second lieutenant, chaplain, gunner, and some seamen perished in the flames; but the greater part of the crew was saved. The Merlin was abandoned and destroyed.

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RE:
Who "won" in the battle of Red Bank? The Americans or the British?
This battle was about American soldiers stopping the British and the Hessians from capturing New JErsey forst near the Delaware River. Who, The Americans or the British, won that battle?

Answer: The Americans.

The Battle of Red Bank during the Revolutionary War was fought and won at Fort Mercer which was situated north of the Whitall House on the 400 acre Red Bank Plantation.
The decisiveness of the victory was a vital morale booster for the American troops.