Listeners vary in their ability to understand speech in adverse conditions. Differences in both cognitive and linguistic capacities play a role, but increasing evidence suggests that such factors may contribute differentially depending on the listening challenge. Here, we used multilevel modeling to evaluate contributions of individual differences in age, hearing thresholds, vocabulary, selective attention, working memory capacity, personality traits, and noise sensitivity to variability in measures of comprehension and listening effort in two listening conditions. A total of 35 participants completed a battery of cognitive and linguistic tests as well as a spoken story comprehension task using (1) native-accented English speech masked by speech-shaped noise and (2) nonnative accented English speech without masking. Masker levels were adjusted individually to ensure each participant would show (close to) equivalent word recognition performance across the two conditions. Dependent measures included comprehension tests results, self-rated effort, and electrodermal, cardiovascular, and facial electromyographic measures associated with listening effort. Results showed varied patterns of responsivity across different dependent measures as well as across listening conditions. In particular, results suggested that working memory capacity may play a greater role in the comprehension of nonnative accented speech than noise-masked speech, while hearing acuity and personality may have a stronger influence on physiological responses affected by demands of understanding speech in noise. Furthermore, electrodermal measures may be more strongly affected by affective response to noise-related interference while cardiovascular responses may be more strongly affected by demands on working memory and lexical access.