Ummm - Phi Phi:
Spectacular scenery, very laid back beaches and resorts on the less visited and sheltered east coast, some good daytrips around the island, good partying in town despite low season, some seriously good discounting of midrange and upper properties on booking sites, fairly easy to access from an airport (Phuket or Krabi).
Samui - better weather normally in Sept as said, huge range of midrange and better properties, better shopping and clubbing, good daytrips, more commercialised and western although there are still some very relaxed beaches, can fly right on to the island from Bangkok, Phuket, Singapore, KL.
For budget travellers, I reckon the neighbouring islands of Phangan and Tao are more suitable. But Samui is okay - I'm going back after many years in August.