I'm seeing some suggestions about increased maneuverability. Well... no good can really come of applying real-world science to Star Wars. Case in point, get ready to fall asleep:
Aerodynamically speaking, the change in configuration would have a negligible effect on maneuverability or, if anything, could make the X-wing LESS maneuverable when flying in an atmosphere. In sciency terms, maneuverability is the inverse of stability; if a plane is more stable, it's less maneuverable, and vice versa.
So first we look at the TOP wings. If we look at the design of most real-world private and commercial airplanes, the wings are constructed with a slight upward angle--referred to as "dihedral"--when viewed from the front. This is the greatest contributor to stability on the roll axis of an airplane because the inward tilt of each wing's lift vector tends to roll the plane back to a wings-level attitude.
Next look at the bottom wings. Since someone's already mentioned the Harrier, let's use that: The Harrier's wings are built with a heavy downward angle--or "anhedral." This makes the aircraft extremely maneuverable, which implies a huge loss of stability due to the outward cant of the lift vectors.
The result seems like an equal and opposite effect on maneuverability: the dihedral top wings negate the effect of the anhedral bottom wings, leaving us with an unchanged situation.
BUT--without jumping too far down yet another aerodynamic rabbit hole--the addition of another wing plane adds a complication suffered by real-world biplanes, in which the top wing tends to undermine the lift of the bottom wing, leading in THIS case to a net increase in stability--in other words, a net decrease in maneuverability.
Ergo, under the shackles of real-world science, the change in wing configuration has, at best, no effect, and at worst, a negative effect on the X-wing's maneuverability. Best to just drink the koolaid.