For those who are struggling with which option to choose for a pool bottom, here is my experience with using 1" tongue & groove polystyrene foam.
I installed it as a base directly on the flat ground (no sand). Taped all of the seams and used peel-and-stick foam cove. Worked great, loved the feel of the bottom, the smoothness, cleanliness of install, etc.
This year, the 2 year old liner developed a 5 inch split along the seam at the bottom during the winter. During the spring melt, the ice in the pool turned into a big "ring" of ice. As the water leaked out, this ring of ice settled onto the foam, destroying most of the sheets, in many spots smashing right through to the ground. The water also made it's way under the foam, washing out and displacing some of the ground underneath. The washout was not major, but enough that the foam would need to be removed to fix.
As I am now in the middle of making my repairs, I have decided not to use the foam bottom again. One of the reasons for this is the expense. Even though this scenario probably will not happen very often, the thought of it happening again and having to spend $100+ on foam and Gorilla Tape and spending hours cutting the new pieces is not appealing. Mostly because in my mind I will assume this will happen over and over (even thought it probably wouldn't), and if I used any other bottom there would be little to no expense getting the pool back up and running aside from some labor to straighten things out.
What I have decided to do moving forward is to add 1" of sand in place of the foam, put a Gorilla Pad/Liner Shield or the like on top of that with cove. I should also note that the cheap cove I bought two years ago cannot be re-used either, as it has compressed to about 1/4 the size it was when installed. I will need to replace it with something better.