Why use RAM IC over EEPROM IC?
EEPROMs are slow to write (milliseconds) and they wear out after a certain number of writes (reads are generally unlimited, with exceptions). You can wear an EEPROM out in a very short time if you're writing to particular locations continuously. 

For example, this 1Mbit 24C1024 has a write time that can be as long as 5ms and a 'typical' life of 10^6 cycles. 

If you write to the same location every 10ms then it will wear out in 2-3 hours.