Anyone care to compare and contrast these varieties? Flavor, cold hardiness, ripening time?

Good question pawpawbill. I'm hoping to try JH Adriatic this year but I don't have Green Ischia. From what I have read especially from Herman JH Adriatic is a superior strain of of the Adriatic family of figs that may include all of the following varieties in addition to Green Ischia. Hopefully others who have them in there collection can answer your question about ripening time and flavor.
 
  Battaglia
  Monstrueuse
  Strawberry Verte
  Paradiso gene strain
  Green Greek (not White Greek)
  Ventura
  Chico Strawberry
  Verte                                                                          

Can only speak from the Ischia Green side of the discussion(never had a JH Adriatic)...The IG has survived 7 winters(N.J. winters), inground, with no die back whatsoever...the fig is yellowish/green on the outside with strawberry red inside(when fully ripe)...the only drawback for a N.J. grower is that it dosen't ripen until late September which is already drawing to the end of our growing season here, so not all the figs make it to fully ripe (when they are ripe the taste is very sweet(like strawberry jam)...the tree is a great producer(350 figs this year)...many of these figs were used to make fig jam and fig jelly(about 50 jars total) because they never made it to dead ripe.

Frank FMD has grown and I'm sure eaten both of these. Hopefully he will chime in here. I have small plants of both and will have an answer in a few years!

ForeverFigs,

Thanks for the report on IG I have a long growing season and like the cold hardiness.

JH Adriatic is cold hardy here. No need protection here after 2 years. I left my potted tree outside.

what zone Paully ?

Zone6/7 -- Pacific Northwest, British Columbia, Canada

The Green Ischia if kept in a sheltered spot does fine in zone 7. My JH Adriatic's in a pot so I can't address that part of your question.
I really like both these figs but If I HAD TO choose I favor the Jh A just a bit more.
The GI I have is the most vigorous growing fig I've ever seen. 
My JH A is only 3 years old so I'm not sure about exact ripening time but last year they were both ripening figs later in the season.
Ooops! Just ignore the other picture - I don't know how to delete and it has the same number as the JH A for some reason. But just 4 info -- that row of figs is about to go dormant as you can see by the changing leaf color.

Both figs look great, but very similar. You notice any difference in the fruit?