Spectra of young benchmark brown dwarfs with well-known ages are vital to characterize other brown dwarfs, for which ages are in general not known. These spectra are also crucial to test atmospheric models, which have the potential to provide detailed information about the atmospheres of these objects. However, to test atmospheric models optimally, medium-resolution, long-wavelength-coverage spectra with well-understood uncertainties are ideal, such as the spectra provided by the NIRSpec instrument on board the James Webb Space Telescope. In this paper, we present medium-resolution JWST/NIRSpec spectra of two young brown dwarfs, TWA 28 (M9.0) and TWA 27A (M9.0), and one planetary-mass object, TWA 27B (L6.0), members of the TW Hydrae Association (age ~10Myr). We show the richness of the atomic lines and molecular bands present in the spectra. All objects show signs of a circumstellar disk, via a near-infrared excess and/or via emission lines. We matched a set of cloudless atmospheric spectra (ATMO), and cloudy atmospheric spectra (BT-Settl) to our NIRSpec spectra, and analyzed which wavelength ranges and spectral features both models reproduce best. Both models derive consistent parameters for the three sources, and predict the existence of CH4 at 3.35{mu}m in TWA 27B. Nonetheless, in contrast to other slightly older objects with similar spectral type, like PSO 318.5-22 and VHS 1256b, this feature is not present in the spectrum of TWA 27B. The lack of the CH4 feature might suggest that the L-T transition of very young dwarfs starts at later spectral types than for older brown dwarfs.