CITATION I FLC BECOME CONFUSED WHEN N90 DEP CTLR INSTRUCTS PLT TO TURN TO A HDG THAT IS DIFFERENT FROM THE SID HDG.

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WHILE DEPARTING TEB RWY 24 VIA THE TEB 5 DEP AND CLBING THROUGH 1000 FT MSL; WE WERE HANDED OFF TO NEW YORK DEP. DEP ASSIGNED A HDG OF 260 DEGS; WHICH DIFFERED FROM THE 285 DEG HDG ON THE SID. THE SID REQUIRES A CLB TO 1500 FT AGL; THEN A TURN TO 285 DEG HDG; MAINTAIN 1500 FT MSL UNTIL PASSING THE TEB 4.5 DME; THEN CLB TO 2000 FT MSL. I WAS DISTR BY THE DIFFERENT HDG ASSIGNMENT IN THE TURN AND CLBED TO 2000 FT MSL AT APPROX 3.5 DME TEB. ATC QUERIED OUR ALT; AND WE IMMEDIATELY CORRECTED TO 1500 FT MSL. THE FLT CONTINUED NORMALLY FROM THAT POINT. THAT DEP REQUIRES VERY CLOSE MONITORING IN A JET BECAUSE OF THE HIGH SPDS AND SHORT TIMES INVOLVED BEFORE THE LEVELOFF AND TURN. I ALLOWED MYSELF TO GET DISTR BY THE DIFFERENT HDG. COPLT WAS ON THE RADIO WITH ATC AND COULDN'T WARN ME IN TIME. FATIGUE WAS A CONTRIBUTING FACTOR AS WAS THE ACFT MODEL. BECAUSE OF A MECHANICAL WE WERE FLYING AN OLDER CITATION I; THAT WE HADN'T FLOWN IN A FEW MONTHS; AND THE WORKLOAD AND INSTRUMENTATION IS VERY DIFFERENT FROM THE CITATION II WE NORMALLY FLY.