The only real similarity between these two visions of the criminal justice system is that both of them exist (according to Packer) within the general framework of the United States Constitution.
Packer argues that the two models are very close to opposite in their aims. However, they both believe in and adhere to the standards set out in the Constitution. For example, both models believe that the criminal justice system must operate within some set boundaries. Not even the most avid backer of the crime control model would argue for a police state such as that of Nazi Germany -- one where there were no limits on what authorities may do.
So the major similarity is that both models accept the ideas of the US Constitution, even if they do not agree on exactly how those ideas should be applied.