Tunnel-injection lasers promise advantages in modulation bandwidth and temperature stability in comparison to conventional laser designs. In this paper, we present results of a microscopic theory for laser properties of tunnel-injection devices and a comparison to a conventional quantum-dot laser structure. In general, the modulation bandwidth of semiconductor lasers is affected by the steady-state occupations of electrons and holes via the presence of spectral hole burning. For tunnel-injection lasers with InGaAs quantum dot emitting at the telecom wavelength of 1,55$mu$m, we demonstrate that the absence of spectral hole burning favors this concept over conventional quantum-dot based lasers.