Coffee is a lot more than caffeine, though. It contains a whole family of monoamine oxidase inhibitors, which have a host of effects on the nervous system.
That said, Red Bull very likely contains several types of flavonoids that also act as MAO-B inhibitors.
Coffee, on the other hand, contains both MAO-A and MAO-B inhibitors mainly from the Harmala alkaloid family. Some of the compounds are neurotoxic.