On the far side of the Atlantic the commanders who may be forgotten:

British General of the 7 years war

General Sir William Johnson

He was Chef Indian Agent for the Crown as well as a military commander and can be said to also have founded the American Rangers.

The American Revolution:

On the American side one could say that the war was won in spite of the generalship. Most were incompetent at best. Washington though had to play politics with the various Colonies to keep the army together, meaning that he kept these guys for political reasons.

The ones worth mentioning as competent or better are:

Washington
Benedict Arnold
George Rogers Clark
Nathaniel Greene
Daniel Morgan
Francis Marion
Friedrich von Steuben (drill master/trainer)
Mad Anthony Wayne
Henry Lee

In my estimation Clark was their best man but was strictly a frontier commander, though he did defeat Arnold ,after his defection, a distinction held by no other American commander. (the battle its self was an ambush but that is no mean feat given the commanders involved)

Arnold was the victor of Saratoga even though Gates received the credit and was in Washington’s estimation his ablest commander until his defection.