The petitioner/plaintiff has to start the lawsuit.
The defendant/respondent has to answer the lawsuit (or be in default).
So if I had to pick, I'd want to be the one who started the lawsuit since I could make it go more my way.
"...Hey there, I have a quick question: In a no-fault,
essentially uncontested divorce is there any practical difference between being the petitioner or the respondent?...."
I've never seen an uncontested divorce.