Their use for PC BIOSes means SPI flash has become insanely cheap - Spansion have 4mbit parts for GBP0.11 and 32mbits for GBP0.27 in 100x qtys at Digikey.
For a read-mostly application, there's little to choose between flash & eeprom in terms of performance. SPI flash is 3.3v (or lower) only, and can read much, much faster than eeprom if that's what you need - tens of megabytes per second are possible using fast clocks, QSPI and DDR modes.
Where you're writing, things get more complex, and you need to look at your requirement in detail. EEprom has a moderate write time (mS to low 10s of mS) to write up to typically 64-256 bytes.
Flash has faster writes (a few hundred uS to write up to 256 bytes) to already-erased pages, BUT very long erase times (many tens of seconds to fully erase a big device) , and large erase page sizes (typically 64K, sometimes as low as 4K), which can mean very big "dead" times which preclude things like continuous streaming unless you have plenty of buffer RAM to cover the erase time. One possible way round this, as they are now so cheap, is to simply use two devices, so one can be writing while the other is erasing.
These days the only reason to use EEPROM would be if you need small write granularity, 5V operation, or a small SOT23-6 type package for small capacities, or want to have an I2C interface. Otherwise SPI flash is likely to be cheaper for any significant (>64kbit) capacity.