Any Arduino or ‘Arduino Compatible’ board should work with the software. One limitation is that there must be enough pins to operate all of the peripherals FarmBot needs. A different board would likely need a different configuration file in order to map the functions to the right pins, though that is a minor detail that could be accommodated for very easily.
The main reason we’re using the MEGA/RAMPS combo is because it is the most common combo for the set of abilities we need, and for that reason it has the most community support and greatest availability. Most DIY 3D printers use this combo, and it is only when one needs more motors, higher current, or desires a different form factor do they move to one of the other boards out there, and yes there are a lot! Here is a partial list.