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To identify promising exoplanets for atmospheric characterization and to make the best use of observational data, a thorough understanding of their atmospheres is needed. Three-dimensional general circulation models (GCMs) are one of the most comprehensive tools available for this task and will be used to interpret observations of temperate rocky exoplanets. Due to parameterization choices made in GCMs, they can produce different results, even for the same planet. Employing four widely used exoplanetary GCMs-ExoCAM, LMD-G, ROCKE-3D, and the UM-we continue the TRAPPIST-1 Habitable Atmosphere Intercomparison by modeling aquaplanet climates of TRAPPIST-1e with a moist atmosphere dominated by either nitrogen or carbon dioxide. Although the GCMs disagree on the details of the simulated regimes, they all predict a temperate climate with neither of the two cases pushed out of the habitable state. Nevertheless, the intermodel spread in the global mean surface temperature is nonnegligible: 14 K and 24 K in the nitrogen- and carbon dioxide-dominated case, respectively. We find substantial intermodel differences in moist variables, with the smallest amount of clouds in LMD-Generic and the largest in ROCKE-3D. ExoCAM predicts the warmest climate for both cases and thus has the highest water vapor content and the largest amount and variability of cloud condensate. The UM tends to produce colder conditions, especially in the nitrogen-dominated case due to a strong negative cloud radiative effect on the day side of TRAPPIST-1e. Our study highlights various biases of GCMs and emphasizes the importance of not relying solely on one model to understand exoplanet climates.