"Witness the victory of the echo over the voice." - Shinzy had a HUGE inferiority complex, because of his shitty life in Reman mines, because he's "just" a clone. And through his incredibly twisted worldview, saw the solution in utterly annihilating Picard's life, his world, any trace of his comparitively cushy, easy, privileged life. He wanted to bring humanity down to his level, so to speak. Show them what it's like to live without comforts of Earth and the Federation.
Is it really any less believable than Hitler's quest to exterminate the Jewish?
Well, yes, because Hitler was a member of a privileged oppressing group, not an oppressed group. It just doesn't make sense that Shinzon would direct his genocidal urges at anyone other than the people who had actually enslaved him.
you're assuming that Shinzon's motivations have to be rational. I think the Hitler analogy is actually a decent one. Hitler had no personal reasons to hate Jews, and his "racial theories" were the worst sort of pseudoscientific garbage. And, having fought alongside Jews in WWI, he KNEW that the "stab in the back" was a myth.
Shinzon may have had no RATIONAL reason to hate Picard and to take "revenge" by going after Earth, but the "resentment of the voice by the echo" thing makes a twisted sort of sense from a psychopath's point of view.