Various diets work better for various people (stating the obvious but true). All diets work, it's mainly about can you stick to them for long enough to make a difference/ become a semi permanent change in your way of eating.
PCOS tends to respond well to low carb. It's worth reading about the science behind it (try Gary Taubes 'what if it's all been a big fat lie'). The reason for high fat with low carb is partly that is makes it bearable for long enough for the body chemistry to do its thing, you are much less hungry with high fat and it means there's always something you can eat e.g cheese, boiled egg etc
Low carb with low fat is hard to stick to, you will be very hungry, and so tends to work best as something like Fast 800 - a short sharp reset rather than a permanent change.
When I first read about low carb high fat I honestly thought the author was mad. My reaction was 'but that goes against all the advice' (the advice being lots of low fat starchy carbs, with tiny amounts of fat, and that all calories were equal so as long as you stuck to your calorie limit, for weight loss it didn't matter if 100% of your calories were from chocolate). Then I thought ... but you're sticking to the 'advice' and you're fatter than ever ...so it must be worth a try.
And it was. I lost 3 stone fairly effortlessly as long as I stuck to it, including eating out at least once every week, sometimes twice, I just learned what I could have from various menus and stayed away from carby sides, the bread basket and puddings, although I did sometimes have cheese.
What is most striking is the lack of hunger once you're in the zone. Having been a hungry person my whole life, I found myself occasionally skipping meals because I wasn't hungry, and have ended up with a largely 16:8 fasting pattern (again, lots of science about how this is good for the body)