Why would one still use normal EEPROM instead of flash?
To be pedantic, FLASH memory is merely a form of EEPROM: There is a marketing / branding aspect here. Typically, the distinction used today is that EEPROMS are single-byte (or storage word) erasable / rewritable, while FLASH is block-based for erase/write operations. 

Relevant to the question: 


EEPROMs continue to be popular due to maximum erase/write cycle ratings being an order of magnitude or two better than FLASH
Due to investments in design typically having been amortized over time, as with any mature technology, the cost of production and testing reduces compared to a newer technology.