Generally speaking, by filing first you set the tone of the issues that will be resolved in the Dissolution. If there is a disagreement, you will know when the other party files the response. Often times, seeing something in writing changes the landscape upon which a verbal agreement was built. So by filing first you clearly state what your expectations are and how you believe property should be divided and debts assigned.
If there are kids involved, it's another matter. You need to file a PP and child support worksheets in addition tot eh Petition, if there is a dispute, you have the opportunity to get into court before the other party to have a temporary orders hearing or to get ex parte relief if needed -- it all depends on the nature of the dispute if there is a dispute.
Hope this helps
The information is for general information purposes only. Nothing stated above should be taken as legal advice for any individual case or situation.
If things are going "relatively" smoothly, then it may be worth your time to file first in case things do not go as smoothly down the road. While there is no stated benefit to filing first, and filing first is never a sure bet to a positive outcome, it can let you set the tone of what issues will be addressed should things go less smoothly. As stated, there is a charge for filing first, so it's up to you to decide how much control you want over the issues on the table.
There is no legal advantage in filing first. The law is the same whether you file or your spouse files first. There may be some practical advantages of filing first. Most important is that you get the process started instead of waiting for you spouse. The disadvantage is that you pay the filing fee with the court. If you are both agreeable to all the terms and this will not be contested, there is no real benefit or advantage. If things are contested and there needs to be temporary orders, then starting the process yourself is critical. If the case goes to court, the filing party gets to present their evidence first.