Curt,
I was talking with someone about op amps who works for a company that uses the LT1360 in its preamps. We all agree that spec.s don't tell the whole story, but comparing them can often reveal something about a unit's performance. The AD797 that you use has lower input noise voltage than the 1360 (0.9 nv/rt Hz v. 9.0) and lower max. input offset voltage (80 microvolts v. 1 millivolt). However, the 1360 has a much faster slew rate (800 V/microsecond v. 20) and a faster settling time (60 ns v. 800) ...
First let me say something seems to be wrong with my AC email notices, I did not receive a notice of this post, nor did I see this post before someone emailed and brought it to my attention.
OK, now on to your question...
Low noise, low distortion, fast slew rate and settling, high CMRR and PSRR, the phase shift curves, and drive capabilities are all important things to look at when comparing op-amps. But... there are sooo... many parts inside (transistors, diodes, capacitors, etc) that the final test must be a listening test. Many parts that spec well sound bad.
It's good to pick all the op-amps you can find with good-to-great specs and then listen to them, let your ears decide which one sounds best.
Particular attention must be paid to the test fixture to allow the UUT (the op-amp) to achieve it's full potential all the way through to the power amplifier or you could be wasting your time.
In other words, IMO op-amps can not be selected on specs alone.
That said:
The 795 has been designed for audio and special attention and compromises have been paid/made to make it perform best in the audio frequency range. The 1360 on the other hand has been optimized for higher frequency video applications use and I'm sure special attention and compromises have also been paid/made to achieve the desired performance.
Based on my experience I would assume the 1360 would not be a top contender in an audio application. A listening test may prove it is an excellent audio op-amp but IMO that would be an exception to the norm.
