It is sometimes claimed that a draw (a shot that curves from right to left for a right-handed golfer) goes farther than a fade (a shot that curves from left to right for a right-handed golfer).  While some shots that draw may be experienced to go farther than other shots that fade, that is not due to the different directions of curvature of the shots.  First, let's understand why, and then we can understand why draws are often observed to go farther than fades.

Consider three shots hit by the same club with the clubface oriented straight toward a target.  A shot hit with the club path in the same direction as the target will go straight with no sidespin component.  To hit a draw, the club must be moving from an inside to outside direction across the back of the ball at impact (with the clubface still oriented toward the target).  To hit a fade, the club must be moving from outside to inside.  Each of these two shots will have the same topspin and equal but opposite sidespin, so they will curve equal amounts in opposite directions.

It may be useful to consider that a draw hit by a right-handed golfer is really just a fade hit by a left-handed golfer and vice-versa.  It does not matter to the ball which side of it the golfer is standing as it only responds to the input it receives from the club.  It will start in a direction very close to perpendicular to the face, and curve in a direction relative to the spin.  Whether that curvature is to the left or right should not affect distance differently compared to curving the other way (except if one swing direction enables the golfer to generate higher clubhead speed and hit the ball harder).

Assuming equal force imparted to the ball by either swing (so the ball could fly the same distance) the actual straight-line distance of curved shots will be less than for a straight shot because that distance will instead be along a curved path.  Additionally, only the straight shot is hit with the full force of club being transmitted to the ball's direction.  The sideways direction of the club that produces a sidespin component accounts for some of the club's speed, so the forward speed of the club is reduced, meaning distance is maximized with a straight shot.  Aside from this loss of force and the length of the ball's flight not being linear, there is also an affect on distance due to the forces generated by spin.

Aerodynamically, whenever lift is produced, drag is also generated.  This induced drag is inversely proportional to the span of a wing squared.  Longer span means less induced drag, and shorter span means greater induced drag.  That is why airplanes have long wings, and efficient gliders have very long wings.  A ball is a rather poor wing, but when spinning it generates a lift force due to difference in pressure (caused by the variation in velocity) on opposite sides of it.  This means that any curving shot has greater drag due to the additional sideways lift force being created through spin, hence this greater drag will operate to shorten the flight of the ball.

A straight shot will only have topspin, which will generate lift and induced drag, but the lift will only be oriented upward without any influence on changing the direction of the ball, and only induced drag due to that lift will be generated without additional induced drag due to any sideways oriented force.  From this perspective a straight shot is more efficient and offers the greatest distance.

So, if a straight shot should go farthest, and shots curving either way reduced by equal amounts, why do draws often appear to go farther and fades not as far?  The answer relates to how the draw or fade was produced.  Usually, when the claim that draws go farther than fades is made, it is accompanied with an explanation that draws fly lower and fades fly higher.  This is different than merely the effect of sideways curvature, which would not cause the ball to go farther, but really decreases distance.  The issue of a draw rolling farther than a fade after the ball hits the ground is a further complication (which a lower shot can do), but the focus will be on how far the ball flies.

Up (or really down) to a limit, a lower ball flight will fly farther.  That limit is down around the typical loft of drivers (around 10 - 11 degrees) plus a few degrees because a driver actually hits the ball in an upward direction off a tee (with the face angled additionally upward), so around 14 degrees launch angle.  That is a rather low angle and benefits from the lift due to backspin keeping the ball in the air longer.

That draws can be observed to fly farther than fades is not inherently due to the sideways curvature of the ball's flight, but is a byproduct of the change in loft when a ball is hit with the clubface closed or open.  A closed clubface will cause sidespin that influences the ball to draw and the ball will fly lower because when the club is closed its loft is reduced.  An open clubface will cause sidespin that influences the ball to fade and fly higher because opening the clubface increases loft.

It has already been discussed that shots hit with the club having the same face orientation but creating different sidespin by modifying the club's direction across the back of the ball at impact support that a straight shot will fly farthest.  This was because the height of the shot was not significantly impacted by the sideways direction of the club that caused the sidespin and subsequent curvature of the ball with its loss in distance.  Let's now consider shots hit with the same club, but with the face rotated closed or open.

It is important not to connect a change in sideways direction with a difference in vertical height as they may not be related depending on how the ball was hit.  Sideways curvature relates to the difference in the clubface's angle from the club's direction at impact, which opening or closing the clubface effects.  The height of a shot is affected by the loft of the club (and the topspin generated, really backspin), which is altered by opening or closing the clubface.  So, opening and closing the clubface causes two effects - a difference in the height of a shot, and a difference in the curvature of a shot - but only the first can cause the ball to fly farther.

Rather than closing the clubface and influencing the ball to draw, a lower lofted club could have been used to hit the ball straight instead.  Consider for example a six-iron with the clubface closed such that its loft is equivalent to a five-iron.  The ball will depart both at the same angle, perpendicular to the face.  A ball hit by the five-iron will go straight as far as the golfer hits that particular club.  A ball hit by the closed six-iron will have to be started to the outside so it can curve back to the target and will lose some distance due to its curvature, so really the six-iron needed to be closed so its loft was even less than the five-iron.  This seems like a harder shot to hit than a straight five-iron.

Remember, a ball hit straight does not have a component of sideways spin, but a ball hit with the clubface closed relative to the club path does in order for it to draw.  It is the sideways component of spin that generates an aerodynamic force on the ball to cause it to change direction.  That sideways force has additional drag associated with it, which reduces distance.

It could be possible to deloft a club and then hit the ball in the direction perpendicular to the face so that no sideways spin is imparted, and this could produce the same result as a lesser lofted club hit straight (so why bother?). Both of these options would produce a straight shot with the same topspin, launch angle, height, and distance.

Reviewing the popular claim that a draw goes farther; this is not because it draws, but merely because the club was delofted in order to hit a draw, and choosing a lower lofted club would have allowed the ball to be hit straight at least as far, or actually farther because a straight shot is more efficient.

There are good reasons to hit shots that curve - to go around a tree, or to approach the green from a different angle - but distance is not one of them.