You have a very good question. I can share my experience with you. Maybe it will help.
I did have both ovaries removed, and according to both my Endocrinologist and Family Dr, having both ovaries removed makes PCOS easier to treat. The reason given, is because of the cycling of the ovaries. If you keep even one ovary, it is common to need to be on a birth control pill to try to control the cysts. Without any ovaries, I am able to get all of my hormones in balance with diet, exercise, and daily estrogen and spironolactone. I also take synthroid because my PCOS affected my thyroid too
Your concern is very valid. What does your Dr recommend? I have read here where other women with PCOS have kept one or both ovaries, and regretted it because they still had painful cysts.
So, if you keep an ovary, you are likely looking at taking the birth control pill, and if you don't keep either ovary, then you are talking about HRT. HRT has come a long ways, and bio-identical estrogen and progesterone is available at a very low cost, if needed. I prefer the bio-identical HRT to the risks that come with the Birth Control Pill.
The best thing you can do for yourself, in my humble opinion, is to find a Dr, possibly and endocrinologist, who understands PCOS. It has been my experience that not all Dr's who treat surgical menopause really understand that PCOS requires a different level of testing and treatment.
Let us know what you decide and how you are doing.
and Best Wishes for your surgery and recovery,