A had a call from a friend, coming to NYC and thinking of having a little family party at a Jewish deli. He asked my opinion of Katz vs. Second Avenue Deli. Personally, I haven't eaten at either one. I know Katz is considered tops, and I once went there, but was so irked at their prices that I stalked out. But my recollection was that it was one large room, possibly without table service (I think you had to go up to the counter to order), so to my mind not a party-isn place.
Any ideas, any other suggestions? What's Barney Greengrass like? I'm guessing the party would be somewhere between 8-15 people, and at least one of them is older and hard of hearing. Do any delis have small private rooms?