Both the Ramps and Anet LCDs seem to use the same two ribbon cables.

I’m thinking of replacing the Anet mainboard with an Arduino/Ramps 1.4 and it would be nice to keep the same LCD as it fits nicely in the acrylic frame.

The Ramps setup is lower cost and more flexible with more connectors and the big issue is that it has double the FLASH memory

Even they are the same ribbon cables, but pinout are different. You can’t use the straight ribbon cable if are planning to connect RAMPS to Anet LCD. You will need to move the pins around. Or you can get a REPRAP_DISCOUNT_SMART_CONTROLLER, so you will have SD card reader too.