There appears to be a belief in the community that it is important for you to commence proceedings first for custody of the children. Generally speaking it makes no difference whether you file an Application first in Court or whether you are the Respondent in the proceedings. The Response documents give you the opportunity to say which Orders you agree with and alternatively what further Orders you are seeking that were not in the Application.
In saying this though, if you are about to do something that you think a court may frown upon, eg. breach a Court Order by withholding the children or removing the children from their school etc then it is important to demonstrate to the Court that you have filed in the Court before you take unilateral action if possible. If the other parent files first then it may look like you were not attempting to obtain permission of the court before simply doing what you want.