Having flown both DL and ITA (as well as pre-Ita-AZ) many times on both JFK-FCO and -MXP, I can jump in with experience (although, come sempre, YMMV). Each has advantages and disadvantages that I've experienced.
ITA, advantages:
- better soft product in J (esp meals and wine), about equal in Y from what I hear
- if you are or speak Italian, more professional service... usually
- lower prices it seems, for both ex-Europe and ex-US on same routes
ITA, disadvantages:
- few options if something goes wrong (mechanic, crew issue); poor to no skyteam integration
- No MQD for DLM members (but MQM, only if booked through DL)
- Difficult assistance line/communications centre, even if you speak Italian - much more difficult if not
DL, advantages:
- very good reliability and options if there are problems: much more dependable that you will arrive around your scheduled time
- good tools for rebooking, etc., especially for higher-level medallion members who have priority
- lounges and service at JFK
DL, advantages:
- cabin crew can be hit-or-miss: have had wonderful FA, surly and uncaring FA, and some who seemed to be fresh off the farm and couldn't figure out how to walk down the isle.
- food is sub-par in all classes, but especially J - makes BA look like sophisticates... and don't get me started on the wine
Regardless, you'll have access to the same lounges if you've status with DL (though not with ITA) *or* are flying J. The ITA lounges seem to have improved in the last month or two; DL lounges are ... spartan.
Mutatis mutandis, I would book with DL because of reliability and MQD, but if it is a really good deal, ITA.