It might have been that Concord go the title because the TU never actually started passenger service?
First one (Tu-144A) does look different (no canards, other cockpit window layout).
PhotosAfter the Le Bourget crash they made a few adjustments (most visible one: Canards) and they had them in service for a few years between Moscow and Almaty.
For the rest, just the basic russian approach: if it doesn't go fast enough, put a bigger engine in it (
Tu-144D (few built, high tail numbers, Simsheim has one) had more power compared to the
Tu-144S (main service model, flat exhaust)
According to the NASA guys that worked with the test program that involved both Concorde (not flown by NASA because there wasn't a plane availiable) and the Tu-144LL, the tupolev had better landing characteristics (less work needed to keep the nose up when the main gear touched), but the different engines that actually didn't quite fit made a mess of the throttle controls