I have stayed in Patong but not at the HI. I have stayed at the Holiday Inn Resort on Phi Phi. There is no comparison between the two locations. Patong is crowded and lively day and night. HI on Phi Phi is the opposite. Bear in mind that the location of HI on Phi Phi is on the deserted side of the island. There is no town, only a couple of resorts and a local restaurant. It is a long boat ride to any night life. Most of your meals will be taken at the resort. The resort has a bar and offers limited entertainment. There is decent snorkeling off the beach at you front door. There are some excursions offered during the day.
All that being said, the HI on Phi Phi is one of the quietest most relaxing and pleasant places I have ever stayed.