That is a tricky question. People used to think that there really was an advantage to filing first, because you could sort of pick which court you ended up in. When you file in Tarrant County, the courts are randomly assigned. It used to be that if you filed and you did not like the court that you ended up in, you could dismiss your case and refile. However, we are not allowed to do that anymore, so that aspect of it has been taken away.
Today, the benefit to filing first is that you are in charge of the train, so you can set your hearings. You can drive the train and keep it going. As the respondent, you can still come in and do that, but it is a little bit harder.
On the other hand, if you are the petitioner, which means you are the one that filed, you are usually the one who is tasked with drafting all of the orders. That, in turn, means you are going to be paying more in attorney fees because when you hire an attorney, you are paying for time. If your attorney is drafting an order, they are spending more time on your case.
In my opinion, there are benefits sometimes to letting the other party file because they are going to spend more in attorney fees. Whether you want to file first depends on your goals and what it is you are trying to accomplish.