Thanks for this post! I visited Sukayu Onsen twice, last time being in January this year. This is a great onsen which I like a lot.
Nowadays, the two large baths are officially "separated" by a virtual line, men being asked to stay on the left side, while women can enjoy the right one. The bathing area is thus equivalent for both genders.
Here is a picture of the main bath house, taken from the official web site of the onsen :
By the way, there are other baths in the hotel, but they are normally only for people staying overnight. There, more amenities like showers and shampoo are available.
There are also some detailed information on Sukayu Onsen on the Secret Onsen