is parallel preferable over SPI?

It's case by case.

SPI is fast when drawing to consecutive addresses.
The results for ColorBarTest and ColorTest represent this.

However, REGISTER I/O parallel is faster when drawing to non-contiguous addresses.
This is useful when you use a lot of text.
Because text fonts draw to almost non-contiguous addresses.

Performance comparison using ILI9341(240x320)

SPI used this.

The biggest advantage of using a parallel TFT is that there are clearly more types of devices than SPI.

from esp-idf-parallel-tft.

Oh wow. Thank you so much! I can see what you mean - it literally is a case of picking the display that best suits the application.

Fonts really are a bind. I developed a couple of high performance variants of the Adafruit GFX routines for my last project and fonts are truly a cluster ... of pixels. That's one of the reasons I've moved from the ATMega328p from that project to the ESP32 for the current one (two actually).

Given that I'm sorely tempted to investigate customising the PCB to carry a full-sized parallel Arduino HAT. There's already a Streamdeck-like design with an TFT mounted in place but I haven't managed to get my hands on one yet to see if it will work for these projects which are aimed at schools.

from esp-idf-parallel-tft.