If you ask most people they will tell you that Ta'anis Esther is much more lenient than Tisha B'Av. After all, Tisha B'Av has the 5 restrictions and the Rema paskens that pregnant and nursing women don't have to fast on Ta'anis Esther. However, it is not so simple.
There is a machlokes Rishonim what the m'kor is for Ta'anis Esther. Some say it is a minhag patterned after the 3 fasts that Esther and Mordechai imposed on B'nei Yisroel before she met the king. However, the Ra'avad brought by the Ran in Ta'anis Perek 2 learns it from the posuk "divreio tzomos v'za'akasom". The Ra'avad is understood to mean that Ta'anis Esther has the status of Divrei Kabbala, just like the mitzvos of Purim.
The question is, what is the status of Ta'anis Esther when it is a nidche. The Avnei Nezer writes that the status of Divrei Kabbala only applies to 13th of Adar. When the fast is pushed back to Thursday, the 11th of Adar, it is a regular takana d'rabanan. The Avnei Nezer clearly understands that a ta'anis nidcheh is a different takana and is not tashluimin for the original fast. The Shvus Ya'akov disagrees and says just like we darshen "z'manim tuva" tolearn you can lein the megilla on the 11th thru 15th of Adar, we also use the drasha to tell us Ta'anis Esther can be the 11th of Adar m'divrei kabbalah. One could argue, that the Shevus Yaakov agrees with the Avnei Nezer in principle that that a ta'anis nidcheh is a different takana and is not tashluimin for the original fast. However, by Ta'anis Esther we have a drasha telling us the nidche fast is included in the divrei kabbalah. However, by other fast days-like Tisha B'Av, he would agree it is a lesser status than the original fast.
The halacha is that a Ba'al Bris can eat when Tisha B'av is nidcheh. How about on Ta'anis Esther? According to teh Shvus Yaakov one could argue that Ta'anis Esther that is nidcheh is still divrei kabbala and a Ba'al Bris could not eat unlike Tisha B'Av nidcheh which is a lesser status than the original day.