In terms of the digital summing that is going on in my mixer, if I bring in a high quality stereo signal from another source  (and digitally at that)  I can pass this through to my main stereo output buss and monitor the signal there.  I can also easily monitor the input signal.  When I switch back and forth comparing those two signals, they sound identical to me.  (tone wise but especially the stereo width of the mix)  But I guess I am not summing either at this point.  Just passing a two channel signal from one point to another.  It does show perhaps the stereo output buss of my mixer is not messing with signal integrity in any way.
 
There is something else that may be going on here as well. So far no processing on any of the stereo stems has been implied. Every input and output in the Yamaha has access to a 4 band parametric EQ and a dynamic effect that can come from a list of over 40 types. By leaving off any processing you may do over a stem say inside your DAW, turn it off and send it to a digital mixer instead. Do some of that work there instead.  The EQ and the dynamics sound different to me than anything inside Studio One even. They take on a different character.  The compressor over the stereo buss for example can be set to sound real nice in terms of dynamics control.  Not to mention two outstanding time based effects using hardware algorithms.  This all adds to quite a different sound when all the summing processing options are utilised within a digital mixer.  Some digital mixers such as the newest Yamaha range add in lots of analog modeling and processing now. Neve has helped design some of these plug-ins and I have heard they sound excellent.
 

This relatively simple article sort of explains it I think:
 
https://theproaudiofiles.com/analog-summing-perceptual-preferences/
 
Both forms of summing can sound excellent and a good mix engineer should be able to create a great mix using both approaches. 
 
Genres are involved. We now have two options as to how things can end up sounding.  Electronic music is one genre that really benefits from all digital summing.  I can get a higher degree of separation with digital summing in electronic music for example.
 
If you add multiple sources of well recorded acoustic sounds (eg great marriage of source and mic choice plus preamp) ie adding very warm smooth individual sounding tracks then to the overall mix, that end mix will still be warm and smooth sounding. It does not have to be harsh at all. It will only end up harsh if you let it.  It is all about using your ears, EQ and keeping things sounding nice and under control.  All possible in a digital summing environment. 
 
Software is getting interesting now too. The fact they can model analog synthesisers so well must also apply to emulating analog summing. Spend some time inside Harrison Mixbus and you will find out how nice it can all sound. 
Console emulators, tape saturation etc. Its all great and can be used so wisely now too.
 
What is great is now you can have a mixture of analog and digital sounding tracks and buses eg stems. You don't have to put your entire mix through the analog summing process like you are forced to do when doing all analog summing.  Now parts of your mix can have that sound and other parts a more pure digital pristine type of sound.  The digital side of things can sound like digital and analog now.  The analog side has still only got one sound option.
 
We are getting more choices now. You just have to learn to master them that is all.  Mastering digital just requires you to spend a lot of time in it and researching all the latest digital trends is also a must too. 
 
 
 
 
 
 
 

ampfixer
Most of this discussion is way over my head. When I do some music that I really care about and want others to listen to, I take one extra step. I mix to stereo and then bounce it out to my Teac tape machine. Then I record the tape back into Sonar to create the final track. I have no idea if this is analogue summing, but it does seem to make it sound really good.

"Analog summing" basically means you "mix" or "sum" a number of channels together in an analog mixer instead of inside Sonar. Often in practice it means sending only your buses to be mixed together to the final two tracks in an analog mixer or dedicated analog summing device with a limited number of channels and very few controls.
 
For example, instead of routing each bus in Sonar to the Master, you instead send them each out to an analog mixer/summer to be be combined into two tracks that then go to the Master in Sonar.

There will always be a group of people who have excellent ears but will have difficulty telling apart say an analog sum mix and a digital one. That fact alone means it is very even in terms of how they both sound.  It is not one way or the other.
 
Check out this video from Universal Audio on the 88RS channel strip.  
 
http://www.uaudio.com/blog/neve-5-minute-tips
 
You either believe in this type of development that is going on or you don't.  I am a believer and love the sound of this stuff now.  Once you agree that it sounds good (and many very well respected engineers have said so) then what is to hold back the concept of being able to digitally model a beautiful analog summing mix perfectly.  I think in many ways we are here now.  (eg Studio One latest console shaper plugin. You have control over the crosstalk among other things)
 
I find in electronic music the fact that separate channels of audio for example (of synths of course) can combine digitally but in a way they remain more separate until the very point where the complex analog wave is produced (eg to feed your monitors) In an analog console the voltages are all meeting and combining sooner that is one aspect of it.  But even in an all digital world I have hardware instruments for example and mix them using an analog console. You can create the analog summed voltages type of sound quite early on. And stay there for as long as you want to.  I get a better produced sound overall with the synths by actually finally rendering each one at a time and combine the audio tracks digitally.  I find this to me allows me to place and almost hear them individually on a slightly clearer level. Hard to describe. Some of them end up being turned down.  Maximum illusion, minimum voltage.  The clarity is also there from not having to be recorded on tape and being played back either. Another unnecessary analog step being involved.
 
Punch is better in an all digital world. Percussive transients have never sounded better. As a drummer I have always found tape can never playback the snap that exists in the real kit live. Digital has solved that issue now and transients sound amazing. More punch in fact. You can hit faster and harder now too.