JB3 is obsolete.
They are both "stage 3"
JB4 is a more sophisticated board and uses CANbus to communicate with the car. To keep things simple it provides safer and more consistent power then the JB3 and its full a many other features.
Their website description really says it all:
"Now shipping with JB4 featuring 5x the processing power, 2x the memory, more robust signal conditioning, and integrated CANbus. Our new CANbus module allows the JB4 to communicate with your vehicle like never before. New features include code reading/deleting, optional in dash boost, timing, air/fuel, shift light, and IAT gauges, autotuning, a buttery smooth new CANbus based integrated boost control system, map switching on the fly via steering wheel controls, built in downpipe fix, hot/cold oil temperature protection, progressive methanol integration, water pump remapping, gear dependent boost control/traction assist, and much more to come with free firmware updates uploaded using a windows laptop (or mac w/ windows emulator) and BMS USB cable."