The number of write cycles most EEPROMs can handle generally far exceeds the number of write cycles most flash memory can handle.
EEPROMS can generally handle ~100,000-1,000,000 writes per cell.
Flash is generally rated to ~1,000-100,000 writes (it varies heavily depending on the type of flash).
Another advantage EEPROM has over flash is that flash generally has to be erased in blocks, so if your write patterns involve sequential single-byte writes, you will use many more write cycles on the flash memory then you would with the equivalent EEPROM, as EEPROM memory can generally be erased on a per-byte basis, rather then the per-block erase cycle flash uses.
Basically, flash generally is erased in blocks of ~64-512 kilobytes. Therefore, for every write anywhere within that block, the controller has to erase the entire block, using a write cycle for the entire block. You can see, if you sequentially performed single-byte writes to each address in a block, you would wind up performing anywhere between 64K to 512K writes to the entire block, which could easily use the entire write endurance of the flash.
As such, EEPROMs are generally used in situations where the local processor is small does not have the ability to buffer writes to each flash page.
A lot of this is becoming less true as flash technology advances. There are flash memory ICs that include the facilities for local write-buffering, as well as the write-endurance on flash memory increasing dramatically.