The board looks like a Xylotex or one of the copies. A lot of these were bundled with Taigs, mostly with motors that were horribly mis-matched to it. It is based on an older Allegro chip. At was an ok board when nothing else was available but is very out dated now. It can only handle about 2 amps and 24-30 volts.
Don't go blindly changing motors without understanding what you have already otherwise you are just throwing money away. What is the rating of your current motors? Are they the old round can type or the newer square motors? Do you have any specs on them? The important specs for steppers aside from holding torque are current and inductance. From the inductance, you can calculate what voltage the motor is happiest at. The motors in a lot of the Xylotex packages were fairly high inductance and would have needed 80 volts or higher to run their best. That had a lot to do with the poor performance of a lot of those packages.
Quite often smaller motors will give you better performance since power drops off quickly as the speed increases with larger motors. This is especially true when you have a fine pitched lead screw like the Taig does. Taigs perform really well with motors in the 160 to 225 oz/in range at about 48 volts.
Depending on which motors you have already, you would probably get more bang for your buck by upgrading the controller and power supply. A Gecko G540 with a 48v 7a power supply is what I would recommend. Be wary of the eBay 4 axis packages from China. A lot of them are not very reliable according to threads I have seen on CNC Zone.
There are a lot of threads on CNC Zone on matching motors and controllers.
If you post a picture of the controller box, someone might be able to recognize the package.
God luck and enjoy your Taig. It is a good little machine.
bob