Cessna Citation Sovereign (C680)
Flight Crew Private; Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Last 90 Days 100; Flight Crew Total 550; Flight Crew Type 25
Confusion; Situational Awareness
Conflict Airborne Conflict; Deviation - Altitude Crossing Restriction Not Met; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Returned To Clearance
Human Factors
While departing on the TEB RUUDY 4 DEP; we received both a traffic advisory from ATC and from our TCAS system about a plane flying below us; opposite direction.  I was the pilot flying and elected to keep my nose down at about 1400 feet in order to maintain visual separation with traffic.  The RUUDY 4 calls for 1500 feet until WENTZ.  TCAS was telling us that the plane was about 2 miles away and at 1000 feet or so (or there abouts; things were moving fast!).  The PIC on the plane (I currently hold an SOE restriction) indicated to me after the incident that I should have been at 1500 feet as per the SID.  After thinking about it and interpreting the rules I agree.  My rush to think about keeping visual separation; while important; trumped my thoughts [to] follow the DP as it was designed. We knew that TEB Tower was in contact with our traffic and we were with NY Tracon; so separation was always assured and was never violated in this instance; even despite the lower altitude.  Quick thinking would have yielded better results in this case.  With everything happening so fast; one has to know all the rules of the road to prepare quickly.  They create departure procedures for a reason and adherence to them is paramount; unless in the event of RA advisory which did not occur.  No sooner then I realized I had leveled off too early; NY TRACON has us climbing.  I am now however better prepared for this type of situation and learned more regarding the rules of SID's.
CE680 First Officer reports crossing WENTZ below the RUUDY 4 depicted altitude due to a traffic advisory although the traffic was at 1000 feet.