That's interesting that you didn't find any significant correlations Justin – I wonder if that points to the validity of the Basis at measuring sleep. Sleep quality and quantity tend to correlate highly, and consumer grade devices are generally pretty good at measuring sleep quantity (within a margin of error), although they are known to overestimate a bit.
For example, in this study, the researchers found that the SenseWear (validation study wtih polysomnography: r = .84) correlated strongly with the Misfit shine (r = 0.82, bias = 44 mins), Jawbone UP (r = 0.89, bias = 23.5mins) Withings pulse (r = 0.92, bias = 24.4), and the Fitbit one (r = 0.92, bias = 15.9) in every day settings. As you can see, the correlations (r) are high, but most devices tend to overestimate sleep. The shine overestimates sleep by as much as 44 minutes, and the Fitbit One by just 15 minutes. Conversely, in an older study (n = 23) with the Fitbit One, the fitbit one was only accurate for about half of participants. I'm not sure if the algorithm was updated between these studies leading to the varying results – it's a bit perplexing.
Alternatively, simple worn Actigraph devices have shown high correlations with subjective sleep quality (which is what Alan seemed to be particularly interested in). In a study using a GT3M actigraphs for example, my colleague reported a correlation of about .88 (p < .01) with subjective measures of sleep quality (n = 113) – where sleep quality was measured via the Pittsburgh Sleep Diary. This suggest that subjective measures of sleep which merely ascertain perception of sleep quality are pretty accurate. So more complex testing might not be necessary.
So to answer @Dr_Mush's question, I'm not sure what specialised devices are particularly most accurate right now, but in our research we simply use the Pittsburg Sleep diary for subject insight on sleep quality – which is surprisingly accurate. In an upcoming study we will use consumer grade devices (i.e., Fitbit One) to get an estimation of within-person variability in sleep quantity, which according to the aforementioned studies are reasonably accurate at estimating duration of sleep in healthy adults.