Some linguists have tried to distinguish between these words by suggesting that nearly applies to time, space, or quantity (nearly midnight, nearly at his destination, nearly enough money) and almost to degree (almost nothing, almost dead). This distinction hardly seems worthwhile; in the illustrations given here, almost and nearly are interchangeable. If you wish to think of nearly as a positive word representing an approach and almost as a "minus" word subtracting from an idea, all right, but the difference seems too subtle for ordinary common sense. It is true, however, that in referring to one's state of mind or feeling, almost is preferable. One is almost afraid to do something, not nearly afraid. See also almost.
Dictionary of problem words and expressions. Harry Shaw. 1975.