The throughputs for SPI interface that can be used for coprocessor mode in CY7C67300 is up to 12 Mbit/s.
HPI is a popular choice because of the speed at which it can move data. The throughput with HPI is up to 16 MB/s. Both of the serial interfaces, SPI and HSS, are much slower due to the serial nature of the interface and the additional overhead required for a serial interface. However, depending upon your application, the SPI serial interface is still adequate and is desirable when connecting to a system processor that has the same serial interface.