It depends. In the eyes of the court, the Plaintiff (the spouse who files the Complaint initiating the legal process of the divorce) and the Defendant (the other spouse) are not seen differently by virtue of who files for divorce. Often times in divorce actions, lawyers and judge dispense with the formal titles of Plaintiff and Defendant when discussing the case and use Husband and Wife or Father and Mother.
That said, your attorney may advise you to file first or to wait until your spouse files, depending upon the overall strategy for your case and your circumstances. For example, if you are separated from your spouse but have a beneficial temporary arrangement, your attorney may counsel you to wait for your spouse to file. Conversely, if your children live with your spouse, you may want to institute the legal process to allow you to have custody of or more visitation with your children sooner than if you waited for your spouse to file first.
Allow your attorney to support you in making the decision about whether and when to initiate the legal process by filing a Complaint.