Putin’s probably bad news for America and American interests (among other things, Putin loves Iran), but is he really bad news for the Russian people? He’s done a lot to privatize and deregulate Russian industry, and he seems to have concern for Christianity and Christian values (unlike Stalin). In terms of domestic policy, Putin is light years ahead of Stalin.
At this point, it would be hard to tell which person would be more dangerous overall to America, especially since both despised us and neither of them shriveled up into an isolationist ball. Stalin certainly had more to work with and was lucky that FDR was a sympathizer, but I’d argue that Putin is smarter on his own merits. Putin has no need to capitulate to a moron like Hussein Soetoro, especially since they both share the common goal of destroying America.
Russia's problems with Islam are simpler than ours: their Muslim enemies are all Sunnis, so a Shi'ite power is a natural ally against a common enemy. We're stuck with Iranian official hatred as blowback from the Shah having been one of "our bastards" during the Cold War, as well as a pack of Sunni enemies (AQ, ISIS).