The radicalization and devolution of the Chechen insurgency itself represents a politico-military victory for Moscow. Large scale terrorist attacks are the tactics of a militarily weak actor, and the islamisation of the conflict represents a far smaller and more radical support base.
But the original Chechen independence movement was sane and could be negotiated with. The new one was incredibly violent, and represented the spread of the Islam to the North Caucus. That was a failure, in my opinion. The seizing of the hospital in Buddenovsk, an act of terrorism, had nothing to do with the relative military strength or weakness of the Chechen insurgency at the time. What was a nationalist uprising, and could have been satisfied after prolonged negotiations, with wide autonomy (possible less of one then modern Chechnya) turned into a bloody mess.
Yes there's more of it but it doesn't change the fact that Russia failed to effectively fight off the Chechens the first time around. They were in no condition to fight a war at all and their enemies from within sense that weakness and lauched attacks against the state. After that ass beating Russia had to rush itself into being a strong military power in some way or risking total collapse of the whole country. And they also used mental warfare to corrupt the powers that they fighting. That part helped to win the second war. But it was mostly how Russia fought that was the difference maker. You need to understand that otherwise that little detail you put up on here would be meaningless.
That's what I was saying. Russia had to restructure itself before it launched another war against the Chechens. And yes it DID became stronger, especially since the end of the USSR. Though Russia has no chance of eclipsing the USSR in the next 10 years or so.