Do you have a manual (with circuit diagrams) for your existing control box ?
The first product you have linked is a USB driven motion controller and would require extra parts.
The second product you have linked may be a good replacement for your existing controller (using your existing power supply, etc.) and the wiring-up is documented by the supplier. However, please bear in mind that the cheap Chinese products sometimes work OK and sometimes they do not – there is often no backup or technical support from the supplier and you are pretty much on your own.
It costs considerably more but the Gecko G540 (
http://www.geckodrive.com/geckodrive-step-motor-drives/g540.html) is probably the best product you could buy – it comes with all the technical support and backup you would ever need. Again the wiring-up is all well documented and there are plenty of people here who could help if you run into difficulties.
Tweakie.