What are the advantages and disadvantages of a delta wing compared to a swept wing?
Benefits of a delta wing:


Due to the large root chord, a delta wing combines low relative wing thickness with a sufficiently thick wing spar for a lightweight structure. Since a low relative thickness keeps wave drag down (a drag component which occurs only in supersonic flow), this makes delta wings especially attractive for supersonic aircraft.
The large root chord gives the delta wing a high internal fuel volume even at a low relative thickness.
The large root chord also provides it with a large surface area which helps to bring the minimum speed of the aircraft down.
With sufficient leading edge sweep, a delta wing produces vortex lift, so flow separation can be turned into a means of increasing lift.
A delta wing is naturally stable in pitch, therefore it does not require a separate tail surface.


Drawbacks of a delta wing:


The large wing area causes more viscous drag for the same amount of lift compared to a high aspect ratio wing. Swept wings have a better lift-to-drag ratio (L/D) than delta wings.
High-lift devices like fowler flaps are hard to integrate into delta wings. The higher relative thickness of regular airliner wings allows to integrate large flaps more easily, and the rearward location of the trailing edge of a delta wing will produce intolerable pitching moments if such flaps would be deflected.


Generally, the moderately swept high aspect ratio wings of subsonic airliners are ideal for flight at high subsonic Mach numbers. Delta wings are superior only in supersonic flight, and due to their good low speed characteristics they offer the best overall compromise for supersonic aircraft.



North American XB-70 in flight, a classical delta wing design (picture source). Note the canard wing, which has little sweep and a low aspect ratio: This kind of wing is ideal for supersonic flight, provided it has a low relative thickness. The main wing of the XB-70 is a delta wing to keep the take-off and landing speeds relatively low and offers the best compromise of low and high speed characteristics. Also, the wing tips could be deflected downwards to improve directional stability at supersonic speed and to improve L/D by using the waverider effect.





The wings of both the Boeing 787 (top, picture source) and the Airbus A350 (bottom, picture source) show their powerful high-lift devices in these pictures, which allow them to fly with less than half the wing area of a comparable delta wing aircraft. Also, the lower surface area translates into lower drag at high flight speed, and the higher possible wing span helps to reduce induced drag, making those wings far superior for efficient flight at high subsonic speed.