We present a systematic comparison of the main figures of merit for an open-air radio telescope and two different types of enclosed antennas: (1) an ordinary radome, with a metal space frame providing the required mechanical rigidity and a dielectric membrane, and (2) an “astrodome,” i.e., a corotating rigid dome with a large window covered by a tensile membrane structure. The analysis is limited to submillimeter and millimeter wavelengths and large (≳30 m) antenna/enclosure systems, where the window tensile structure is very unlikely to be removable and is supported by either a metal space frame or cable networks. As compared with previous studies of this type, here we concentrate on the specific effects that these large metallic support structures have on sensitive astronomical observations. In particular, we critically discuss how the wind-induced random motions of the metal space frame can limit the sensitivity of continuum observations, as a result of fluctuating shadowing and spillover effects combined with various beam-chopping techniques. Using the Large Millimeter Telescope as a benchmark, we provide baselines for future projects where a similar comparison is needed.