I suppose it depends on what quality of information you are trying to gather from the methods. I routinely use the Nanodrop for quick protein quantitation and follow up with the Pierce 660nm assay for a dependable quantitation. The Nanodrop requires no special reagents, very little sample (1-2uL), and no sample preparation. Furthermore, we leave the machine on at all times so it is always ready to go. The Qubit requires reagents (~$0.85/sample) and sample preparation with specific tubes ($0.15/tube).
Neither machine is high-throughput, which is partially why I like the Pierce 660nm assay in 96-well format. I deal with marine extracts that contain all sorts of absorbing compounds. The protein specific assay is absolutely necessary for my research.