I noticed that some concert shots in similar situations came out surprisingly well with ISO1600 - ok. But for a closer look on that behaviour you can't use just these two pictures...
Do some tests at the same subject, with the same setup. Shoot RAW. And include some over- and underexposed shots in the series. It IS a difference if you step up/down while taking the photo and then correct in the RAW converter. So this maybe already an explanation or at least a start to research further: in the concert ISO1600 shot you have very high dynamic range and nothing in the histogram middle, where things look completely different in #1
Since I do a lot of low light shots I'd be interested in your findings.