What is the difference between TFT LCD interfaces?
The "i80" parallel interface is simple and fast, and can be driven by external memory interfaces on some microcontrollers. However, it's a wide parallel bus, and requires a lot of pins to drive.

SPI requires very few pins to drive, and is available as a hardware peripheral on many microcontrollers. It's slower than the parallel interface, though.

The VSYNC and RGB interfaces are mainly useful for displaying streaming video from live sources (e.g, in a camera). They aren't useful outside special situations.

Given that you're using a PIC32 with what sounds like a big parallel port, the i80 interface is probably ideal.