I have been full-timing for almost 8 years and have stayed in private parks more than state/national parks. The main reason has been due to limited ability to get a site for more than a few days. For example, right now I am at St. George Island State Park in FL. I will stay here a total of 9 days and will have had to move twice.
For many of the national/state parks it seems the weekends get booked far in advance and it tends to lock out full-timers that want to stay longer as is my case. Also, sometimes I will want to stay in an area for a couple of months and the government parks are typically limited to a couple of weeks.
In terms of private park amenities, all I really want is a nice site, either gravel or paved, not overly close to my neighbors, full hookups. I seldom pay a premium for parks with alot of activities.