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In cognitive radio (CR) systems, compressed sensing (CS) has emerged as a promising approach for detecting wireless spectrum that is underutilized (i.e., sparse in the frequency domain). The use of CS techniques is believed to reduce the sensing time at minimal hardware overhead compared to the traditional sweeping spectrum scanner, which is a simple energy detector that scans the frequency bins sequentially. Although the sweeping spectrum scanners can be parallelized to reduce the total scanning time, time-multiplexing is still necessary to cover the very large scanning bandwidth. By contrast, the CS spectrum scanner captures the entire spectrum concurrently to detect the occupied frequency bins. Despite the recent popularity of CS spectrum sensing techniques, no published work is available that rigorously compares the performance of these two sensing schemes under similar hardware constraints and same available total sensing time. This paper makes such a comparison and shows that the multi-channel sweeping spectrum scanner outperforms the CS scanner except at the high input signal-to-noise ratios when the two scanners become comparable. The advantage of the sweeping scanner is that although it observes each frequency bin for a shorter time, each sensing is more reliable and not corrupted by the folding of other frequency bins as in the CS scanner.