You'll need to do a little home work with your control box and whats in it.
What is the power supply voltage that goes to the mks4-v board? Is it 5 volts, 12, 24? You'll have to determine if you need a different supply voltage to power the AXBB (24v ) than what may already be there. IF your current board is 5v or 12 v, maybe you'll find using a UC300eth (5v) or UC400eth (12 v) is easier to install and wire without needing another power supply.
Look at the diagram on the AXBB webpage (
http://www.cncdrive.com/AXBB.html) for 'example' wiring.
You obviously have 3 stepper drives, each drive has a common, step, and dir input required. While your mks4 board has specific 'spots' for each axis drive that aren't user select-able, the AXBB (or UC300 or UC400) do not have any specific required spots to wire to these to, you set that all up in the software (port/pin selection, like Mach3). Same goes for spindle, limit switches, etc).
Any of the CNC drive controls could replace that board you have now, but I think the voltage you have to supply the board might be first hurdle to figure out, then determine if you want the AXBB, or a UC300/400 with a breakout board.
regards
Eric