Veterans who have been exposed to high-intensity blast waves frequently report persistent auditory difficulties such as problems with speech-in-noise (SIN) understanding, even when hearing sensitivity remains normal. However, these subjective reports have proven challenging to corroborate objectively. Here, we sought to determine whether use of complex stimuli and challenging signal contrasts in auditory evoked potential (AEP) paradigms rather than traditional use of simple stimuli and easy signal contrasts improved the ability of these measures to (1) distinguish between blast-exposed Veterans with auditory complaints and neurologically normal control participants, and (2) predict behavioral measures of SIN perception. A total of 33 adults (aged 19-56 years) took part in this study, including 17 Veterans exposed to high-intensity blast waves within the past 10 years and 16 neurologically normal control participants matched for age and hearing status with the Veteran participants. All participants completed the following test measures: (1) a questionnaire probing perceived hearing abilities; (2) behavioral measures of SIN understanding including the BKB-SIN, the AzBio presented in 0 and +5 dB signal to noise ratios (SNRs), and a word-level consonant-vowel-consonant test presented at +5 dB SNR; and (3) electrophysiological tasks involving oddball paradigms in response to simple tones (500 Hz standard, 1000 Hz deviant) and complex speech syllables (/ba/ standard, /da/ deviant) presented in quiet and in four-talker speech babble at a SNR of +5 dB. Blast-exposed Veterans reported significantly greater auditory difficulties compared to control participants. Behavioral performance on tests of SIN perception was generally, but not significantly, poorer among the groups. Latencies of P3 responses to tone signals were significantly longer among blast-exposed participants compared to control participants regardless of background condition, though responses to speech signals were similar across groups. For cortical AEPs, no significant interactions were found between group membership and either stimulus type or background. P3 amplitudes measured in response to signals in background babble accounted for 30.9% of the variance in subjective auditory reports. Behavioral SIN performance was best predicted by a combination of N1 and P2 responses to signals in quiet which accounted for 69.6% and 57.4% of the variance on the AzBio at 0 dB SNR and the BKB-SIN, respectively. Although blast-exposed participants reported far more auditory difficulties compared to controls, use of complex stimuli and challenging signal contrasts in cortical and cognitive AEP measures failed to reveal larger group differences than responses to simple stimuli and easy signal contrasts. Despite this, only P3 responses to signals presented in background babble were predictive of subjective auditory complaints. In contrast, cortical N1 and P2 responses were predictive of behavioral SIN performance but not subjective auditory complaints, and use of challenging background babble generally did not improve performance predictions. These results suggest that challenging stimulus protocols are more likely to tap into perceived auditory deficits, but may not be beneficial for predicting performance on clinical measures of SIN understanding. Finally, these results should be interpreted with caution since blast-exposed participants did not perform significantly poorer on tests of SIN perception.