Wearable in-ear electroencephalographic (EEG) devices hold significant promise for integrating brain monitoring technologies into real-life applications. However, despite the introduction of various in-ear EEG systems, there remains a necessity for validating these technologies against gold-standard, clinical-grade devices. This study aims to evaluate the signal quality of a newly developed mobile in-ear EEG device compared to a standard scalp EEG system among healthy volunteers during wakefulness and sleep. The study evaluated an in-ear EEG device equipped with dry electrodes in a laboratory setting, recording a single bipolar EEG channel using a cross-ear electrode configuration. Thirty healthy participants were recorded simultaneously using the in-ear EEG device and a conventional EEG cap system with 64 wet electrodes. Based on two recording protocols, one during a resting state condition involving alternating eye opening and closure with a low degree of artifact contamination and another consisting of a daytime nap, several quality measures were used for a quantitative comparison including root mean square (RMS) analysis, artifact quantification, similarities of relative spectral power (RSP), signal-to-noise ratio (SNR) based on alpha peak criteria, and cross-signal correlations of alpha activity during eyes-closed conditions and sleep activities. The statistical significance of our results was assessed through nonparametric permutation tests with False Discovery Rate (FDR) control. During the resting state, in-ear and scalp EEG signals exhibited similar fluctuations, characterized by comparable RMS values. However, intermittent signal alterations were noticed in the in-ear recordings during nap sessions, attributed to movements of the head and facial muscles. Spectral analysis indicated similar patterns between in-ear and scalp EEG, showing prominent peaks in the alpha range (8-12 Hz) during rest and in the low-frequency range during naps (particularly in the theta range of 4-7 Hz). Analysis of alpha wave characteristics during eye closures revealed smaller alpha wave amplitudes and slightly lower signal-to-noise ratio (SNR) values in the in-ear EEG compared to scalp EEG. In around 80% of cases, cross-correlation analysis between in-ear and scalp signals, using a contralateral bipolar montage of 64 scalp electrodes, revealed significant correlations with scalp EEG (p < 0.01), particularly evident in the FT11-FT12 and T7-T8 electrode derivations. Our findings support the feasibility of using in-ear EEG devices with dry-contact electrodes for brain activity monitoring, compared to a standard scalp EEG, notably for wakefulness and sleep uses. Although marginal signal degradation is associated with head and facial muscle contractions, the in-ear device offers promising applications for long-term EEG recordings, particularly in scenarios requiring enhanced comfort and user-friendliness.