I have two votes for each. I think that the burgers at Binion's Deli as well as at Oscar's Steakhouse are both awesome. Two much different experiences for sure but you can't go wrong with either choice.
For Pizza, like most of the world, I love Pizza Rock. Great pizza and service each time that we go there. My second choice would be Pop Up Pizza at Plaza. They also offer a different pizza menu at the Sand Dollar Bar at Plaza. That pizza is also made at Pop Up but different options are available there. At least that was the case a few months ago.