With the severe spectrum shortage in conventional cellular bands, millimeter-wave (mmWave) frequencies have been attracting growing attention for next-generation micro-and picocellular wireless networks. A fundamental and open question is whether mmWave cellular networks are likely to be noise-or interference-limited. Identifying in which regime a network is operating is critical for the design of MAC and physical-layer procedures and to provide insights on how transmissions across cells should be coordinated to cope with interference. This work uses the latest measurement-based statistical channel models to accurately assess the Interference-to-Noise Ratio (INR) in a wide range of deployment scenarios. In addition to cell density, we also study antenna array size and antenna patterns, whose effects are critical in the mmWave regime. The channel models also account for blockage, line-of-sight and non-line-of-sight regimes as well as local scattering, that significantly affect the level of spatial isolation.