The Concorde didn't fly supersonically above land, it only could above the ocean. The Tu-144 however flew between Moscow and Almaty, so entirely above land; why did it fly like this? Didn't it have a that loud sonic boom? If no, why not? If it had, why did it fly above land anyway while the Concorde refused to go supersonic above land?
The actual 'legal' reasons have already been mentioned. However, there was a bit more to it.
- Tu-144 was meant to fly over land from the beginning; there was no way around it, unlike Concorde. So it was designed to fly higher. In particular, Tu-144 had about 20% lower wing loading and 20% higher thrust-to-weight ratio (at MTOW) than Concorde. (The reality was a bit more complicated; for example, Concorde was limited to FL600 again for 'legal' reasons, due to certification of the pressurisation system AFAIK).
- Soviet citizens, apart from not being asked their opinion, were quite used to sonic booms from military aircraft. In many places of the country, they wouldn't even raise an eyebrow. In the Urals where I grew up, I heard them almost daily.
The Tupolev Tu-144 was just as loud as the Concorde. As it was already pointed out, the Concorde was legally prevented from going supersonic over land by the US, UK, but it was more than capable of going supersonic over land. There were no similar restrictions over the Soviet Union for the Tu-144. Both planes had a sonic boom.
The plane's chief designer, Alexei Tupolev, whose father Andrei designed the first Soviet jet, was aboard and acknowledged the noise problem, saying it was inevitable with supersonic flight.
"The sonic boom is no different that a thunderclap - so it is no different than nature itself," he said.
From what I can determine, the noise from the Kuznetsov NK-144A turbofan engines that powered the Tupolev Tu-144 were not quiet and comparable to the noise of the Concorde with Rolls-Royce/Snecma Olympus 593 engines at takeoff produced 119.5 decibels. There is no side-by-side comparisons of the noise.
The Tu-144 was much louder inside during flight because of the amount of air it needed to move to keep the skin cool. The Concorde used more advanced cooling methods to keep the interior noise down.
One additional point is that each of the four NK-144A engines produced 6,000 lbs of thrust more than the Olympus 593. Even though the Tu-144 weighed 22 tons more than Concorde, it never really flew at full capacity, so it had a substantial kick during takeoff.
Now if I could just go on a flight with either plane.
Another reason is that much of the flight was over the huge land mass of Kazakhstan with very low population density. So few people live in the steppes there that Roscosmos lets the first stage of rockets taking off of Baikonur simply fall to the ground. You wouldn't want to do that over France or England.1
Population density is higher in Russia close to Moscow, but still lower than in Western Europe, so with a suitable flight corridor most of the flight would be over sparsely populated areas.
1 Bear with me when I divert a little. For details about the first stages falling from the sky in Kazakhstan I recommend the stunning documentary Space Tourists by Christian Frei. One of its threads follows Kazakh metal scrap collectors who hunt them down. You will be surprised what they do with the round bottom part of the fuel tanks on the first evening after finding a stage.