Why is it said that the Tupolev Tu-144 had superior aerodynamics to the Concorde?
Unfortunately, there is no hard data available (at least in open literature) to back up these claims. 

One for the claim may be due to the fact that the Tu-144 was designed to fly higher than Concorde as its primary flight path was over land rather than water. Because of this, the L/D ratio of the Tu-144 was higher than that of Concorde (7 vs 8 in Tu-144D). Also, the Tu-144 was bigger and was meant to carry more passengers.



Photo Courtesy: globalsecurity.org

The Tupolev site offers an interesting explanation for this claim. Basically, they say that despite the engines and other subsystems being inefficient, the Tu-144 performed similar to the Concorde due to superior aerodynamics of the aircraft. The performance of the Tu-144's RD-36 engines was later brought up to that of Concorde's Olympus 593, at least in fuel consumption.

To quote,


  It should be added that the engines were less perfect (by specific parameters the engines of TU-144 a/c were brought close to “Olympus” only in their last modification). All these negative initial data were compensated in the course of development of the project by high aerodynamic cleanness of TU-144 which was achieved by making the design more complicated and by lowering maintainability of the aircraft.


But without any hard data, it is not possible to compare the two aircraft directly.