I've been using op amps for a couple of decades... Having said that, I tell my students that there are some profound differences in the way they handle. Bob Widlar invented the op amp back in the 60s (uA702), and the technique of analog integrated circuits has been improved ever since. I think we spent 8 weeks back in grad school studying just the venerable 741. Saying that op amps from BB sound like tubes is, of course, ridiculous. Tubes sound like tubes because of how they clip and their harmonics.
I personally prefer op amps from PMI (Precision Monolithics), but Analog Devices are right up there with BB. I also believe that BB op amps have been on a steady decline since they were bought by TI. But the bottom line in these audio applications is choosing the right amp for the right application. Also, biasing, filtering, layout make big differences. The op amp configuration is also important, such as true differential topology or even the use of an instrumentation op amp on audio front end circuits.
You see, there is a very close analogy. When I worked for GM as a coop many moons ago, the same assembly line built a Cadillac and a Pontiac or a Chevy. Why was one perceived to be of higher quality then? Its how its treated when it leaves the factory. Same can be said about op amps. People that buy cheap op amps use them in circuits that are not up to par for sound, while a careful engineer may use a better op amp, but the circuit will also most certainly be different. You simply cannot still get away from the base specs of an op amp - but an OP27 from PMI, BB, TI, National, ADI or Maxim must conform to the same specs. How its actually used is then anybody's guess.