Difference between SPI and CSI?
The Serial Peripheral Interface(SPI) and the Clocked Serial Interface (CSI) are essentially the same thing, both synchronous serial interfaces in a master/slave mode with clock, data in and data out leads.  Both use chip select leads to address multiple devices.

The CSI interface is implemented in the NEC/Renesas V850 lines of microcontrollers and appears to be proprietary to NEC.

This document, "CSI to SPI Peripheral Communication in V850ES Microcontrollers" explains how to program the CSI registers of a V850ES microcontroller to interface with various SPI peripherals such as MAX6627 and DS1722. For example, table 2 of the document shows the equivalences between "NEC Electronics CSI Clocking Method", register bits CKPn and DAPn, and "SPI Clocking Method", bits CPOL and CHPA which control the polarity and timing of the clocking.

Although one diagram (Figure 1) in the document shows two clock leads (one in and one out), they are actually the same pin so I think this is just meant to represent the dual functionality of clock out for a master and clock in for a slave, which is the same for both interfaces.

In addition to the  serial clock (SCK), data input (SI) and data output (SO) leads common to both CSI and SPI, CSI has an optional handshake (HS) lead that can be used to control a data transfer much in the same way UART handshake signals RTS/CTS are used.

I don't see any reason why CSI would be preferred over SPI, you are going to see either one or the other depending on the vendor.  The CSI interface as implemented on the V850ES only goes up to 5 Mb/s, whereas most SPI interfaces go up to 25 or even 50 Mb/s so in that regard SPI is a better choice.