The month and the week pull in opposite directions, which is why asking which island is cheaper has no answer. A month of unlimited training runs 7,500 to 9,600 baht across the 3 Koh Samui camps listed here and 8,800 to 10,000 across the 4 on Koh Phangan, so Samui is cheaper by the month at both ends of the range. A week runs 2,500 to 3,500 on Samui against 3,000 to 3,300 on Koh Phangan, which puts the single cheapest week on Samui and the cheaper typical week on Phangan. Privates are the plainest gap of all: every Samui camp charges exactly 1,000 baht an hour and Koh Phangan starts 300 baht below that.
Both islands tell you what things cost, and almost nowhere else in Thailand does. Every camp on both islands publishes a group rate, a week, a month and a private, and no other region on this site with more than one camp in it manages that; Bangkok manages it at 2 camps of 11. Koh Phangan goes further and is close to uniform: 3 of its 4 camps charge the same 10,000 baht a month and all 4 run exactly two sessions a day. Samui spreads 2,100 baht between its cheapest month and its dearest, and the two Samui camps that publish a timetable run two sessions a day and four, so on Samui the camp you pick still decides something.
Season is the one thing that does not separate these two. Both sit on the Southern Gulf calendar, driest January to April and wettest roughly October to December, so a badly timed trip to one island is a badly timed trip to the other, and the usual advice to swap coasts does not apply between them. What separates them is the last leg. Samui has an airport and Koh Phangan does not, so every arrival on Phangan finishes with an open water crossing that rough weather cancels. In the wet months that is the difference between landing and training on the same day and losing a day at each end of the trip.