You can access PSN on 3.60, I got Ape Quest to load an ARK bubble and I can even buy things. Like a certain PS1 game that used to be exploitable and might still be exploitable (Sports Superbike 2).
I think the reason some people go for 3.65 is because some plugins and homebrews only work there (?), I always thought 3.60 was the golden firmware, but something about 3.65 might be useful for some people.
What really bothers me about 3.65 is that ARK will work fine on it, it just needs a (PSP) kernel exploit to run (the K.BIN file in the ARK_01234 folder). Technically the one TheFl0w made for the Trinity exploit chain (the latest h-encore for latest firmware) should work, but I can't seem to get it working.