How to run two LEGO electric trains at the same time?
This probably isn't going to be solved without either changing to remote controlled PF trains or creating a complex control system.

Even if you were able to supply the exact same constant voltage to both trains, they'd both need to have precisely the same motor characteristics, weight, and aerodynamic properties. That's going to be difficult.

One way to address this is to create track blocks that are electrically isolated and can be controlled independently. You can isolate the track sections using tape at the joints, or you can physically cut the metal rails. You could then connect these blocks up to your NXT and build some sensors to determine what speed the trains need to run in these sections in order to not hit each other.