In my case, my STBXWH is "too busy" with his own law practice (which is far removed from family law) to be bothered with doing all the paperwork. By maintaining a very nice, cordial attitude with him, I've lulled him into thinking that I will be very fair and not try to take advantage of anything.
When you file first, you have the opportunity to say what you want first. You get to claim what is your separate property and what is community property. You have the opportunity to request that STBX pay atty fees and court costs. You can also ask that the court not allow him to request spousal support.
He, as the respondent, has 30 days to respond if he disagrees with any of this. If he doesn't, it leads to default, which means he is not contesting what I'm asking for.
Because my "very busy" STBXWH is too busy to read any of the divorce papers served him and is so trusting of me (which he SHOULD be since I've been a loyal, giving, fair, good wife for 25 years), he will be going along with pretty much everything I've asked for.
I've been the one driving the divorce bus. He doesn't even plan on hiring a divorce lawyer until the marriage settlement agreement is filed. Then all hell may break loose, but we'll see. His income outweighs mine by a huge amount, so he knows he's paying, but I've been very careful in trying to manipulate things in my favor by being sweet and nice.
In your case, since you have more to lose financially, you may want to file first to state your requests first and possible have a STBX like mine who doesn't read the fine print. OR if you WH files first, make sure you read and respond within that 30 days.