Well why build one super weapon when you can build two at twice the price.
And lets face it aside from one small flaw the first Death Star would likely have stopped the Rebellion in it's tracks. Why would worlds revolt against the Empire if they could simply be blown up. The second Death Star would likely have elimianted that design flaw.
Besides the Emperor was over confident in his plan to destroy he allowed the location of the Second Death Star to Leak, he allowed the knowledge he was going to be there to leak (Of course he could have gone elsewherr) to the Rebel Alliance, which Luke highlighted as his weakness. As for use of another super weapon not sure it could have worked thematically (at least as the film was written). Basically the Emperor want to gloat over defeating the Rebel Alliance, he could then use that as Properganda
"I lead our forces in crushing the Rebels"