I have an 18 month old daughter and I'm currently looking for work, so this question has been incredibly important.
Essentially, I see three major areas where Lauren impacts my job search:
1.) My time is significantly more important.
2.) Equity is less important.
3.) Stability is more important.
My time is significantly more important because I will only have one child and frankly, I don't want to miss her entire youth while I chase my startup dreams.
Equity is still nice, but I want to make sure that if my daughter has the kind of brain and work ethic that could get her into MIT/Ivy League, she won't have to worry about money. Consequently, I invest heavily in her education...both in an education savings plan and via making sure that she is surrounded by intellectually stimulating activities. As an example, consider daycare. It's relatively easy and affordable to put her in a daycare where the kids sit and watch television all day. It's much more expensive to have her in an environment that will use her imagination and where she is cared for by people with an education in early childcare education. Unfortunately, RSUs or stock options don't pay many bills...
Finally, stability is important because finding a new job is stressful. It's significantly more stressful when you have a little person who can't eat your hopes and dreams!
I hope this helped!