For New York, DST is observed from the second Sunday in March to first Sunday in November. For Sydney, DST is observed from the first Sunday in October to the first Sunday in April. For the sake of convenience, the four relevant Sundays for 2013 are as follows: March 10, Nov 3, Oct 6, and April 7, respectively.
Sorting the dates by groups:
- Jan 1 to March 10: Sydney on DST, New York off DST --> 16 hour difference
- March 10 to April 7: both on DST --> 15 hour difference
- April 7 to Oct 6: Sydney off DST, New York on DST --> 14 hour difference
- Oct 6 to Nov 3: both on DST --> 15 hour difference
- Nov 3 to Dec 31: Sydney on DST, New York off DST --> 16 hour difference
Sources: