Darth Vader was more bi-polar and mentally imbalanced than he was as Anakin Skywalker!
Palpatine had engineered his coup perfectly:
The clones executed Order 66 and eliminated nearly 10,000 Jedi on probably 5,000 worlds. Prior to that, they were dying in engagements with the Separatists anyway.
The Senate ratified his declaration of himself as Emperor and they formulated the new government as some sort of Constitutional monarchy (in theory, not practice of course).
The surviving Jedi, and there could have been hundreds to 1,000 of them, were scattered and on the run. A disinformation campaign laid the blame for the war upon them: Dooku had been a Jedi and it wasn't common knowledge that either he or Palpatine were Lords of the Sith; the Jedi (through Dooku likely) created the Clones, and helped perpetuate the war starting with Geonosis as its initial flashpoint. Thus public sentiment was against the Jedi and the public would turn them in or lynch them at their own discretion.
Palpatine seemed satisfied (in Purge, Dark Lord, The Last of the Jedi novels, and some items appearing in Star Wars Tales comics, Tales from the Empire collected, etc.)
Darth Vader on the other hand, was obsessed with killing all the Jedi, perhaps feeling it would help erase who Anakin Skywalker had been, and the betrayal he helped engineer? He didn't want there to be anyone who could recognize him I guess. That's quite a leap into paranoia, isn't it?