This was posted by the Beretta Premium Gun Manager in MD under the official forum of Beretta on Shotgunworld:

"The difference is that the 687 "Extra" was a model that was exclusive to Premium Dealers and Galleries, with a more intricate engraving pattern and a couple of other differences (elongated trigger guard, wooden pad etc).

The Extra was limited as only a field model and has since been replaced by the 687EELL "Classic", with an updated engraving. It has been restyled again in 2013 and the new engraving will be appearing on the shelves of Premium Dealers hopefully by the end of this year."

I've seen some 687EELL Extras and Classics and they are nicer guns than the typical EELL.