The rollout of millimeter-wave (mmWave) cellular network enables us to realize the full potential of 5G/6G with vastly improved throughput and ultra-low latency. MmWave communication relies on highly directional transmission, which significantly increase the training overhead for fine beam alignment. The concept of using out-of-band spatial information to aid mmWave beam search is developed when multi-band systems operating in parallel. The feasibility of leveraging low-band channel information for coarse estimation of high-band beam directions strongly depends on the spatial congruence between two frequency bands. In this paper, we try to provide insights into the answers of two important questions. First, how similar is the power angular spectra (PAS) of radio channels between two well-separated frequency bands? Then, what is the impact of practical system configurations on spatial channel similarity? Specifically, the beam direction-based metric is proposed to measure the power loss and number of false directions if out-of-band spatial information is used instead of in-band information. This metric is more practical and useful than comparing normalized PAS directly. Point cloud ray-tracing and measurement results across multiple frequency bands and environments show that the degree of spatial similarity of beamformed channels is related to antenna beamwidth, frequency gap, and radio link conditions.