Right. Nerdy EE junk follows- tune out if not interested.
Integrated circuit opamps have a few advantages, and a few disadvantages. The primary advantage is cost: they put most of the circuitry needed to implement your preamp into one single little black plastic package with a lot of legs. The primary disadvantage is they they are designed to be used in many, many different applications (from instrumentation through industrial controls to whatever else), and audio is only one of those- and a very small one at that.
So they aren't optimized for audio. They aren't optimized for much of anything, in fact. But they are as convenient as hell to design with, and cheap- so you can get wonderfully adequate products, and even some stellar ones.
Now with discrete components, you can use different circuit structures (like Class A amplifiers for example), and you can optimize every component in the chain for that particular audio application. You don't have to band-aid around the fact that the circuitry was really designed for something else, and you are just borrowing it.... In the case of mic preamps in particular, you can design front end stages that have orders of magnitude lower noise than you can ever hope to achieve with an integrated opamp. Similarly, you can optimize for distortion, or for bandwidth- and you can implement an output stage that doesn't require compromises on your *input* stage.
Ever notice how some low-end IC preamps get noisier with you drive a heavy load than a light (bridging) one? That's because the heavily loaded output stage heats up the chip, which changes the bias current on the input stage- they are thermally coupled, because they live on the same piece of silicon... The designer sand giveth, and the designer sand taketh away.
With opamp-based design, you are really constrained in what you can do. With discrete design, you can do much more, since every component is under your control- and sometimes that can sound better. In the hands of a good design engineer, it can sound _magnificent_, and the opamp-based stuff would be hard-pressed to match it...
There used to be a handful of companies that produced IC opamps that really were optimized for audio. They're mostly gone now, and while what is left has improved along with the improvement in semiconductor manufacturing processes, there's not much choice any more. So if you want to do something _different_ in your circuit design (like Class A), you go discrete.
There's a rage right now in rechipping older opamp-based gear with the newer, faster, quieter parts that are currently available. And that can help a lot! But even so, the best of the opamp-based mic pres really can't compete with the best of the discrete designs for input noise, distortion, and bandwidth.
Mic pres are the place where this is the most start, since it is critical that you have very high gain with an absolute minimum contribution of noise, nonlinearity, or phase/bandwidth problems. Especially noise. The difference between a good discrete design and a run-of-the-mill opamp design is stark. It is real, it can be heard, it can be measured, and it can be understood, even by a non-nerd! It's not magic, and it most definitely isn't the voices of the angels.
Do you want your whole mixer to be discrete? Hell, no- you couldn't afford it, and it'd me a maintenance nightmare... But for truly critical applications like specialized high-end mic pres, discrete designs can offer some advantages- particularly in the noise arena. You put the bucks where the bang really needs to be.