Nanoscale light sources are being intensively investigated for their potential to enable low-energy, high-density optical communication and sensing systems. Both nanolight-emitting diodes (nanoLEDs) and nanolasers have been considered, based on advanced nanophotonic concepts such as photonic crystals and plasmonic structures, with dimensions well into the submicrometer domain. With decreasing dimensions, light-matter interaction becomes stronger, potentially leading to efficient and ultrafast radiative emission, both in the spontaneous and stimulated regimes. These features have created wide expectations for the practical prospects of such nanoscale light sources, in particular for optical interconnects. In this paper, we examine the limits to the downscaling of LEDs and lasers and ask ourselves which type of source is most suited to ultralow-power optical communications. Based on simple physical considerations on the scaling of spontaneous and stimulated emission rates for semiconductor active regions at room temperature, we analyze the speed and energy limits for nanoLEDs and nanolasers as a function of their size. The role of spontaneous emission enhancement (Purcell effect) in practical nanophotonic sources is also revisited. The main conclusion is that nanoLEDs reach a fundamental energy/speed limit for data rates exceeding a few gigahertz per second, whereas nanolasers with active dimensions in the range of few hundred nanometers may enable direct modulation rates larger than 40 Gb/s at power levels adequate for short-distance and low-energy optical interconnects.