select partially matching filenames

I have two lists of files with slightly different naming conventions

files1 = {"DTideal_circ_def=000um_astX=000um_astY=410um.png","DTideal_circ_def=050um_defX=000um_defY=010um.png"}  files2={"DT120_blur7_Defoc=000um_AstigX=000um_AstigY=410um.png", "DT120_blur7_Defoc=000um_AstigX=460um_AstigY=310um.png", "DT120_blur7_Defoc=000um_AstigX=460um_AstigY=360um.png", "DT120_blur7_Defoc=000um_AstigX=460um_AstigY=410um.png", "DT120_blur7_Defoc=000um_AstigX=460um_AstigY=460um.png", "DT120_blur7_Defoc=050um_AstigX=000um_AstigY=010um.png", "DT120_blur7_Defoc=050um_AstigX=000um_AstigY=060um.png", "DT120_blur7_Defoc=050um_AstigX=000um_AstigY=110um.png", "DT120_blur7_Defoc=050um_AstigX=000um_AstigY=160um.png", "DT120_blur7_Defoc=050um_AstigX=000um_AstigY=210um.png", "DT120_blur7_Defoc=050um_AstigX=000um_AstigY=260um.png"} 

I need to create pairs of files the paremeters of which are matching, i.e. to get

{{"DTideal_circ_def=000um_astX=000um_astY=410um.png","DT120_blur7_Defoc=000um_AstigX=000um_AstigY=410um.png"}, {"DTideal_circ_def=050um_defX=000um_defY=010um.png","DT120_blur7_Defoc=050um_AstigX=000um_AstigY=010um.png"}}