The Germans were far ahead at the beginning of the war and had a huge advance until 1943-44 where things reversed. . They had the first radar units of radar equipped night fighters and 360deg azimuth small antennas radars on the ground already in 1939-40. But not much documentation in English unfortunately. History is always written by the ones that win the wars. ..
German radar was more technically advanced than Britain's. however, as most military historians will tell you, the outcome is rarely about who has the best kit. The Chain Home High and Low systems were basic, but as a component of an integrated air defence system, they became very useful tools, and this system was instrumental in the Luftwaffe's defeat. In comparison, the Germans never really organised their air defence to the same capability. They had reached a point where they were close with the Kammhuber line, but they were still relying on single control units controlling just one fighter. The concept of a plan position indicator never occurred to them and no-one in command ever really had an overall picture of the air battle.