One of only two ways of which I am aware in which the Tu-144 was “ahead” of the Concorde1 was in its use of retractable flap-canards, which increased the lift on the front of the aircraft at low speeds, thus allowing the aircraft’s elevons to be used as flaperons (flapevons?) for increased lift without pitching the nose down uncontrollably, and, thereby, decreasing the required takeoff and landing speeds;2 the Concorde, in contrast, had no high-lift devices at all as produced.3
Although the Concorde’s myriad aerodynamic advantages over the Tu-144 allowed it to take off and land at much lower speeds than the Soviet SST even without any canards, its takeoff and landing speeds (especially the former) were still very high by airliner standards, with a typical approach and landing speed of 160 kts (296 kph; 184 mph), and a rotation speed, at maximum takeoff weight, of nearly 200 kts (370 kph; 230 mph). This made the Concorde require very long runways to take off and land (and required the readdition of afterburners in order to keep its runway-length requirements from being even longer), forced the development of a whole new type of brakes in order to be able to stop the aircraft during a landing or rejected takeoff,4 and greatly increased (due to a] centrifugal force, and b] downforce on the main-gear tyres during rotation) the stress on the tyres, and the potential (and actual) destructiveness of a tyre failure.
Why didn’t the Concorde use flap-canards to further decrease its takeoff and landing speeds?
1: The other being the use, in later Tu-144s, of a non-afterburning turbojet.
2: Despite this, the Tu-144 still had a much higher landing speed than the Concorde, thanx to all its other aerodynamic deficiencies.
3: An improved version (the Concorde B) was planned, which would have included leading-edge droops (as well as larger wings and non-afterburning engines) for improved efficiency in subsonic flight and decreased takeoff and landing speeds, but the Concorde programme was cancelled just as the production line was getting ready to build the first Concorde B.
4: Not that I’m complaining about carbon brakes!