Are aircraft similarly affected by the loss of GPS?
One of factors in this discussion is tossing out "GPS" as a kinda catch-all any PNT (Positioning, Navigation, and Timing) process or system that is supported by GPS. (DHS even has a PNT program.)
In the case of rail transportation I think the "P" is key to maintaining situational awareness of everything that is (supposed to be) moving on the tracks -- for those systems that utilize GPS. So any breakdown in hardware, software, connectivity, etc. could stop the trains.
For aircraft, GPS can be used as a primary navigational aid, or a supplemental service. Because sidings on the airways are so few and far between [ ;-) ], pilots often have more than one way of determining their position and/or path. Broadly, space-based position and navigation enables three-dimensional position determination for all phases of flight from departure, en route, and arrival, to airport surface navigation.
The timing part is seeing more and more use in applications such as land-mobile communications. GPS-provided precision timing makes trunked radio systems more effective.