I've been to Katz's about 4 times within the last year, and several others within the last five years. It's always good, I mean great. Of course, the pastrami; although I've had the corned beef and brisket, and thought they were very good too. I've never had anything I did not like. The last time I was there, my eyes were wandering while the slicer sliced, and I noticed they have chili (as it's a deli, the chili is served with pickles). I asked my guy, "who gets the chili?" He returned with a taste. Now, I'm not going to Katz's, personally, and getting the chili, but I'll tell you, it was quite good. I know a lot of people rag on the bread, and the savvy thing is to go for the club roll, but I don't think the rye is so awful. The pastrami itself is so damp, I think that's what people notice, that the bread gets soggy.
I go, almost always, before 11, and then have no wait and lots of space. Between 11 and 12, it's still manageable.
Katz's is, surely, deli museum. A good deal of its being overwhelmingly busy is that it is a tourist attraction. It is both a relic of the LES and a relic of deli's (abet one of a different era from say Carnegie). To use that awful expression, it is what it is.
BTW, if anyone does find themselves on the Lower East Side, besides Katz's, I highly recommend Pickle Guys at Grand & Essex. Everything is excellent. Great guys running the place. Lotsa samples. Nothing close to it in Chicago.
Think Yiddish, Dress British - Advice of Evil Ronnie to me.