Comparator simple build
Since your computer is being serviced i thought i just run a quick simulation to show you some issues with your idea.


As you can see, the general idea sort of works. If V+ is greater than V- the output voltage drops. However, this is a very crude comparator since a substantial voltage difference between V+ and V- is needed to turn the transistor fully on. As you can see, the output voltage is not very close to 0 V in most cases. But if this is sufficient for your application, i guess you can consider it as a working comparator. On the other hand, you could also just use an op-amp as a comparator.