Electronic devices may be provided that contain wireless communications circuitry. The wireless communications circuitry may include radio-frequency transceiver circuitry coupled to multiple antennas. Signal strength measurements may be gathered using the antennas and corresponding signal strength difference measurements may be produced to reflect which of the antennas is exhibiting superior performing. The signal strength difference measurements may be filtered using time-based averaging filters with different speeds. Corresponding filtered difference measurements may be compared to antenna switching criteria such as antenna switching thresholds. An antenna switching threshold may be adjusted in real time based on computations of how much variation is exhibited as a function of time between the difference measurements filtered using the filters of different speeds. Information on device movement or other data may be used in making threshold adjustments.