What are situations to use an actual EEPROM over using emulated EEPROM in flash?
In most cases, the big difference is endurance (the number of write cycles before the cells wear out). EEPROM cells are made to withstand ~ 10k .. 10M cycles, FLASH cells are rated more like 100 .. 10k cycles. (Numbers from memory, no recent research)

Also, FLASH often requires larger blocks to be erased than EEPROM.

Note that we are talking about FLASH and EEPROM on a micro-controller chip, not about separate chips.