First of all it´s about analog and digital equipment used in a studio. You can mix music entirely on a computer (aka “in the box”) these days. There is actually no need of analog gear except from a AD/DA converter (converts analog audio signals into digital audio signals and the other way around).
In the early days, when there have not been computers in a studio, it was all analog. Huge analog consoles and lots of analog audio processing electronics. So there are actually two domains: analog mixing and digital mixing.
The big benefits we have today is to combine best of both worlds. And in this case we are talking about a “hybrid studio”. In a hybrid studio setup is most commonly a computer the center of the whole production. But next to the computer there is also analog outboard gear used to take over on specific reasons.
Advantages of analog gear
Even we have lots of possibilities in recreating and emulating special sounds on a digital basis, there are always some reasons to use the original analog gear once in a time. And the main reason is “character”. Analog gear does react to the sound in another way than digital software does. Depending on how hard you hit analog gear with an incoming signal it may add distortion and / or saturation to the signal in a musical way. Especially when it comes to compressors for example. Using an analog compressor is something else than using an digital compressor. What does not mean that digital compressors aren´t good, they are just different.
Disadvantages of analog gear
The special character of analog gear has some disadvantages where working in the box is a lot easier. First of all it´s the possibility to recreate an earlier setting. Or just a recall of an earlier setting. When it comes to software driven equipment you can easily save your settings and reload it every time you need it. On analog gear you have to take notes or photos of the settings and you have to save them anywhere. To reset the settings you have to pull up these notes and you have to go through every single parameter to set it up the way it was before.
The next disadvantage is simply space. Analog gear might take a lot of space. And when you just need it once in a while it´s just a lot of dead space you could better use for something else. Next to the space, the price is also a big disadvantage. Real good analog gear just has still it´s price. It´s the purchase, the maintenance and the electricity.
Advantages of mixing in the box
Mixing in a box has definitely it´s advantages these days. Once you are familiar with it and know your DAW (Digital Audio Workstation) in and out you really can make a lot of really good sounding music just on a laptop. The entrance into it isn´t that expensive as it would be on analog gear, you need less space and you can always save and open it up again.
Disadvantages of mixing in the box
But even when it´s so much easier in some cases in the box there are also some disadvantages. To get the best out of it you really need to know how to use it and how to create a good sound. Sure it is the same when it comes to analog gear but one of the problems of mixing in the box in this case is the huge amount of possibilities. Let´s take the example from above: a compressor. In an analog studio you might have a couple compressors and you have to decide about what could benefit the most from it. In the box you could easily use 10 different compressors on every single channel. But does that help? Certainly not.
When you use analog gear it adds a certain sound to a specific signal. It may do things to the audio that just sound good, even you don´t know what this thing is actually doing. An audio signal in the box is what it is. It sounds like the mic or the DI box has captured it and you need to dial a couple things in to make it sound really good. Don´t get me wrong both worlds assume some knowledge, but it feels like the analog domain is a little more natural than the digital domain what might make it a little more easier to achieve a sound that we are used to.
Combining both worlds
Luckily we are in a good situation these days. We don´t have to limit ourselves on one of both worlds. We can just hook them up together to mix in a box WITH analog outboard gear. And in my humble opinion this is the best we can do these days. When can mix a complete song in a box but when it´s necessary we can easily add analog character to it on the flight. And that is what a hybrid studio matters. A computer in the center of it all and some selected analog gear to add in to taste.