The opinions of an economist are worth very much, because listening to them sets up situations were it is easy for someone with an economics degree to push an agenda. But economists do have a lot to offer with observations like "this is very similar to the [suchandsuch incident] of [1887] in [Somewhere]", which is worth listening to. The limitations that surround economic 'experiments' are so severe it should be treated more like history and less like physics. Thomas Piketty with Capital in the 21st century is a great example of what I'm thinking - more history and data than theory, but some theory to provide structure to the data.
If science has a measure of quality, then that quality is the accuracy of its predictions. That ties in very closely to the ability to conduct experiments and collect accurate data. Economics as applied is a highly political process, which hampers both the perceptions and reality of how fair the experiments are.
Difference: There's scientific evidence for the experts opinion in all these cases. Economics? That's more or less just crystal ball reading with a scientific shim on the top.