Field-effect transistors based on single-walled carbon nanotubes (SWNTs) and graphene can function as highly sensitive nanoscale (bio)sensors in solution. Here, we compare experimentally how SWNT and graphene transistors respond to changes in the composition of the aqueous electrolyte in which they are immersed. We show that the conductance of SWNTs and graphene is strongly affected by changes in the ionic strength, the pH, and the type of ions present, in a manner that can be qualitatively different for graphene and SWNT devices. We show that this sensitivity to electrolyte composition results from a combination of different mechanisms including electrostatic gating, Schottky-barrier modifications, and changes in gate capacitance. Interestingly, we find strong evidence that the sensor response to changes in electrolyte composition is affected by a high density of ionizable groups on both the underlying substrate and the carbon surfaces. We present a model based on the (regulated) surface charge associated with these ionizable groups that explains the majority of our data. Our findings have significant implications for interpreting and optimizing sensing experiments with nanocarbon transistors. This is particularly true for complex biological samples such as cell extracts, growth media, or bodily fluids, for which the complete composition of the solution needs to be considered.