We present angular resolved photoemission data of the quasi-one-dimensional metals K0.3MoO3 and (TaSe4)2I. The measured conduction band dispersions reflect the highly anisotropic nature of these materials. However, no clear Fermi-Dirac cutoff is observed in the spectra above the Peierls transition, being due to either charge density wave (CDW) fluctuations or due to electronic correlation effects in one dimension. The experimental conduction band width of (TaSe4)2I agrees well with a tight-binding calculation, suggesting a description as a conventional Peierls system with CDW fluctuations suppressing the spectral weight at the Fermi energy. In contrast, the spectra of K0.3MoO3 show an excitation which along the direction of highest conductivity ("easy axis") disperses 5 times faster than expected from band theory. This anomalous increase cannot be explained by electron-electron or electron-phonon interactions in a Fermi liquid scenario, but can be accounted for as holon dispersion in a Luttinger liquid framework, which need not conflict with the material's CDW properties.