There are not a lot of actual code differences between the original SFC and SNES releases. What differences there are I have mostly documented at https://ff4-documentation.readthedocs.io/en/latest/versions.html. Certainly nothing that directly affects difficulty like algorithm changes.
There are some (sometimes significant) changes to stats of the various monsters that you can look up at https://ff4kb.aexoden.com/info/monsters/. As Rivers mentioned, this especially affects the endgame. Some of the late game bosses and monsters had their agility and/or HP significantly reduced for FF2US (and some even more so for Easytype, which was a separate version released in Japan with all sorts of minor changes).
The removal of the abilities and battle items largely serves to make the game simpler, but more difficult (if you know how to utilize those abilities or items). It does however make inventory management much easier.
On balance, for the first time player, I'd say FF2US is somewhat easier, but nothing insurmountable. For more advanced players or speedrunners, the difference narrows but FF2US's moderate endgame advantages still make it a bit easier.
I thought we had a rule about this, but I don't see one, so I guess not. I can tell you that my console can take upwards of 17 seconds to fully clear out its RAM for a hard reset, so for fairness any time used on an emulator should be comparable to that. But like I said, I thought we already had an agreed upon number, so maybe someone else will pipe in.
For NoCW and No64, turbo/non-turbo is a separate sub-leaderboard. For PC, it's a flag you set in the run itself, and is listed as a separate column in the leaderboard. If you're seeing something different, all I can suggest is clearing your cache and reloading.
I suspect most people just really don't like the load times of the PSX version, which I've heard are quite bad, though I've not played it myself.
Has anyone given any thought to standardizing the speed used, or at least providing a field for display of this information? The one run on here with any video at all seems to be running at max speed (either in DOSbox or ScummVM, I couldn't tell.)
If you look at the King's Quest V leaderboard, you'll note it has fields for the emulator used and the cycle count. (Their standard seems to be Max cycles, by the way. Quest for Glory seems to have standardized on 10000 cycles.) I kind of like picking a standard that doesn't depend as much on CPU speed, but with at least one existing run that went on Max, that might be harder. (By my timing, on my PC, Max cycles is about 3 minutes faster than 10000 cycles.)
I haven't submitted any runs, but I have been doing some offline and plan to submit one in a day or three.