Any game that relies on uninitialized memory.
The RAM can hold any random values when powering on, and unless the game writes a value to every RAM slot at boot (AKA initializing the RAM), the values will be different every time you play the game. Final Fantasy doesn't initialize RAM and uses an uninitialized RAM slot for seeding its random number generator (RNG). The N8 also needs to use the RAM for the menu where you select what game on the SD card to play. When starting a game on the N8, the RAM will have the exact same values as the N8 menu left it with (since the console is still powered on) and Final Fantasy will get the exact same number to seed its random generator with every time you start it. In other words, Final Fantasy will not be random at all, but predictable.
Final Fantasy speed-runs relies on a certain value in the random generator by power-cycling the game until you get what you want (you can tell by what first random encounter you get I think). Since the number is always the same at every boot on the N8, you might never be able to get it if played on N8. Therefore it can't be used for speed-runs.
In other words, the problem is that the N8 chain-boots games via a menu, which never happens if you have the original cartridge. A solution would be if the N8 could randomize RAM again right before booting a game, to simulate the natural randomness of the RAM in a fresh cold boot.
