Is Putin Russia's Obama, as well?
None of them is a man in charge. Both of them think of themselves as being "in charge". And maybe some "voters" even support that idea. But that does not change matters for those who didn't vote for or support them (including all foreign citizens). For them, Putin/Obama are just bullies from high school. Most of the time they don't have to do anything with your life, but sometimes their associates in form of judges/cops/army/etc are coming to you and forcing you to do things you don't approve. E.g. sponsoring a war, or "national project", or having your money diluted by inflation or something else.
Both of these men have a great deal of the power of command and control in their respective countries. The recent leaks have made it also very clear that they are "overseeing" heh. As for leadership that's a sticky subject that is way too philosophical for me to touch right now.