FLT CREW OF B757 EXPERIENCE FAULTY CRM AND CHKLIST PROCS WHEN THEY ENCOUNTER A FLAP DISAGREEMENT ON ARR AT ZZZ.

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I WAS THE CAPT AND PF. WHEN I ASKED FOR 'FLAPS 1 DEG' WE GOT AN AURAL WARNING AND EICAS CAUTION MESSAGE 'LEADING EDGE FLAP DISAGREEMENT.' I THEN CALLED FOR THE ABNORMAL CHKLIST AND THE FO READ AND PERFORMED THE CHKLIST WHILE I FLEW THE AIRPLANE AND TALKED TO ATC. I REQUESTED A LEVEL OFF AT 6000 FT MSL AND A DELAY VECTOR. I WANTED AND THOUGHT TO ASK THE FO IF HE WAS RUNNING THE CORRECT CHKLIST BECAUSE I THOUGHT THAT FLT CTL CHKLISTS WERE TRICKY. I DID NOT ASK SPECIFICALLY; BUT I DID QUERY HIM ABOUT THE FACT THAT WE WERE NOT 'PUSHING' THE 'ALTERNATE LEADING EDGE FLAP' SWITCH. HE DID NOT RESPOND. AS I WAS TRYING TO SEE WHICH CHKLIST HE HAD; I GOT A 'STICK SHAKER' STALL WARNING BECAUSE THE SPD BRAKES WERE STILL OUT AND THE AUTOTHROTTLES HAD NOT MAINTAINED REF AIRSPD. AT THAT POINT I CONCENTRATED ON FLYING THE AIRPLANE. THE REST OF THE APCH WAS FLOWN AND WE LANDED UNEVENTFULLY EXCEPT THAT ATC AUTOMATICALLY DISPATCHED EMER RESPONSE VEHICLES. WE FLEW FINAL APCH AND LANDED WITH VREF +30 KTS. WE TAXIED UNEVENTFULLY TO THE GATE AND I DISCOVERED THAT WE RAN THE 'LEADING EDGE FLAP ASYMMETRY' CHKLIST INSTEAD OF THE CORRECT 'LEADING EDGE FLAP DISAGREEMENT' CHKLIST. I POINTED THIS OUT TO THE FO AND HE FELT BAD BUT NOT AS BAD AS I DID. IT WAS JUST AS MUCH MY FAULT BECAUSE I DID NOT DO WHAT WAS REQUIRED TO ENSURE THE CORRECT CHKLIST WAS RUN. THE FO SHOULD HAVE POINTED TO THE EICAS MESSAGE ON THE SCREEN AND THEN POINTED TO THE HDG ON THE ABNORMAL CHKLIST TO ENSURE THEY WERE BOTH THE SAME. I THINK WE FELT RUSHED BECAUSE WE WERE CLOSE TO LNDG AND DID NOT DO THE THINGS REQUIRED TO SLOW THE SIT DOWN. I SHOULD HAVE ASKED FOR A VECTOR FOR A DOWNWIND AWAY FROM THE ARPT AND THEN TOLD THEM WHEN WE WERE READY FOR A BASE TURN.