From looking around at code on the internet, numeric constants are not really used at all. They don't fit very well into javascript, as it is not typed, so it's easier and shorter to just write the constant (1) instead of the (node.MY_CONSTANT).

IndexedDB recently made the change to a enum of strings.

http://lists.w3.org/Archives/Public/public-webapps/2012JanMar/thread.html#msg814

The disadvantage is that numeric constants are sadly used elsewhere. So it's more consistent continue as they are now. However, using enumerated strings will make the code much more readable and obvious.