The task of processing speech masked by concurrent speech/noise can pose a substantial challenge to listeners. However, performance on such tasks may not directly reflect the amount of listening effort they elicit. Changes in pupil size and neural oscillatory power in the alpha range (8–12 Hz) are prominent neurophysiological signals known to reflect listening effort; however, measurements obtained through these two approaches are rarely correlated, suggesting that they may respond differently depending on the specific cognitive demands (and, by extension, the specific type of effort) elicited by specific tasks. This study aimed to compare changes in pupil size and alpha power elicited by different types of auditory maskers (highly confusable intelligible speech maskers, speech-envelope-modulated speech-shaped noise, and unmodulated speech-shaped noise maskers) in young, normal-hearing listeners. Within each condition, the target-to-masker ratio was set at the participant's individually estimated 75% correct point on the psychometric function. The speech masking condition elicited a significantly greater increase in pupil size than either of the noise masking conditions, whereas the unmodulated noise masking condition elicited a significantly greater increase in alpha oscillatory power than the speech masking condition, suggesting that the effort needed to solve these respective tasks may have different neural origins.