Recently ate at both these places.
The pastrami at Katz's is obviously the best in the city. I think few would dispute that. Therefore, if you're looking for a pastrami sandwich with nothing else, Katz's is the way to go. Thick, juicy, and absolutely delicious. Some of this difference is definetly do to the hand slicing, which gives a bigger cut, and probably keeps the juices in a bit better.
Is Katz's a Jewish deli though? I would venture no. Second Ave. is a real Jewish deli. You can walk in to Second Ave., order any Jewish item, and I guarantee you it is among the best in the city. Katz's to me is a one trick pony. They make an amazing pastrami sandwich. Their other stuff is certainly good, but pales in comparison to Second Ave. (and remarkably expensive). I'm talking about Matzo Ball soup, Corned Beef, Fries, Chopped Liver, pickles etc.. (Katz's hot dogs happen to be good as well, but you can find much cheaper dogs with the same quality)
Katz's lacks the Jewish deli atmosphere. I like the warmness and homeliness of 2nd Ave. This is obviously a very subjective judgment, but there's something about Katz's that just doesn't sit well with me.
Another problem I have with Katz's is the pricing. A pastrami sandwich is $12.45. (A sandwich and soda at Katz's will set you back more than $15 after tax). A pastrami or corned beef sandwich at 2nd Ave is $10.75. Add to this the fact that 2nd Ave provides a larger sandwich that is kosher (which probably increases meat costs by at least 50%) and you have the makings of a relative rip off.
If I'm grabbing something quick, I'll take Katz's, but for a meal, there is no comparison: 2nd Ave.