There were actually two Chechen wars and they were fought differently. The First Chechen War was fought with the regular Russian Army being used indiscriminate

There were actually two Chechen wars and they were fought differently. The First Chechen War was fought with the regular Russian Army being used indiscriminately against Chechens. Instead of intelligently targeting the separatist forces, Russian tank columns simply shelled Chechen cities. Despite the heavy death toll (into the 100s of thousands), the Chechens won a semi-autonomous republic in the terms of the ceasefire. The Second Chechen War began when Putin was installed following Yeltsin. The Chechen republic was predictably corrupt and poor following the devastation of the first war. Stupidly, the top military commander of the Chechens, Shamil Basayev, launched an incursion into the neighboring republic of Dagestan. Putin was then able to 'finish the job' in Chechnya. The Russian strategy in the second war was different—they used the intelligence services and local proxies to fight the war rather than depending primarily on army conscripts. They installed a Chechen named Ramzan Kadyrov in as the head of Chechnya, and he fought the separatist Chechens working hand-in-hand with the Russian FSB (successor to the KGB). The second war was a success for the Russians—they had a reliable client in Kadyrov, the Chechen strategies got more desperate (e.g. the seige in Beslan), and the top commanders of the separatists were betrayed and killed (Aslan Maskhadov and Shamil Basayev principally). The Chechen separatists are still out there, but the fighting is very low level. Their current commander, Doku Umarov, hasn't led a major assault on Kadyrov or Russia yet. I don't think the Chechen cause rose or fell with their popularity. I think it had more to do with the anti-insurgent strategy pursued by Russia.