I've done both. I actually stumbled upon being a sitter. I did about 1 year of work (CNA) in skilled nursing/long term care, and then got hired to an agency that staffs hospitals and nursing homes. The agency paid about the same as I was making in skilled nursing. Most of the time I was sent to hospitals as a sitter, and the PP is correct that you're not supposed to read or sleep while watching the patient. As far as I know, from previous replies to threads from nurses, those jobs are being phased out to cut costs. They will hire people who are not certified so the pay grade can be cheaper for the hospital. I actually liked being on the floor better than being a sitter in the hospital because the night went faster.
Right now, after three years of bouncing between hospital work (agencies are a pain to deal with, most of the time for me), and skilled nursing, I ended up in home health. I love it! I can spend the time with my client that I always wanted to in facilities. There is way more downtime, and it's better on my body. Right now my client and family are extremely nice, and the pay is very good because they are paying privately. Recently my client had a UTI (chronic condition using catheters a lot), and so lost mobility during the hospital stay. The family is paying me to be at the rehab facility for a few hours per day, as a sitter, when the daughter isn't there.
In my experience, during the night shift, it's unpredictable how much free time anyone can have. I used to study at night, but I wouldn't depend on having down time to study. Some nights can be like a three ring circus haha. Good luck. PM me if you have any questions if you need to.