I've only eaten at Katz's once and I look forward to my eventual return.
I agree with BK that in spite of how good it is, the pastrami must remain a close second to one's first place. In BK's case, it's Langer's. Sadly, I've never eaten there, so in my case, it's the long lost Carnegie Deli on Seventh Ave. in Manhattan.
But Katz's is a little different. In spite of being so well known, it remains a neighborhood joint and eating there is an adventure. It's off the beaten track for tourists and its main attraction for them is as a filming location, notably the "I'll have what she's having" scene.