That's a damn good question!!
Altho it's really a personal preference that many decide on. It depends on what you have and how you work. Some people dont mind using the mixing features in DP and mix all the tracks thru a stereo out of whatever hardware interface they may have. It's just like having an external mixer really..the external mixer goes out stereo as well..the thing about external mixers whether they are analog or digital is that you have your hands on the faders..most old school people like that feel. Obviously having a digital mixer means you get to keep your digital recording in the digital realm..which keeps the sound pure and clean(Altho sometimes I think digital is "too" clean!) Also with digital mixers you can usually have a MIDI out that can be programmed to control the faders in DP which gives you ua double advantage..you can mix in DP yet still have your hands on the faders and get that real time control instead ofusing a mouse. A lot of companies are making fader packs or new digital consoles that will have templates to control whatever software you might have.
Another thinkg about external mixers is that you may bring all individual tracks out of DP(providing you have the interface for that to happen and the inputs available on your mixer) into the mixer and control every track via the board. Again, it's really a matter of preference to the individual user. I presonally dont mind mixing in the program..I use an external fader pack(teh Tascam US428) to bank thru all the channels and control individual faders so I dont have to use a mouse. Check out the variety of options available and see what suits you best
Opus

From an ergonomic point of view, I don't mind mixing in the program either, though part of me does miss the feel of physical faders under my fingers...I'm more concerned about sound quality, specifically the relative accuracy/robustness of mixing algorithms in DP versus those in a digital board, versus the summing circuitry in an analog board. What mixing method gives the best clarity, detail, low-end solidity, imaging, and headroom?...he wondered.

Well, I'm not hearing a great big difference between using DP as a level changer and using my Mackie D8B. I may be able to convince myself that the Mackie sounds a bit better, but then again that may be my wallet whispering in my ear. I keep meaning to borrow a little Allen & Heath or something, and trying a straight fader/pan type mix both ways. I'll definitely post if I do.

Originally posted by Brian Middleton:
From an ergonomic point of view, I don't mind mixing in the program either, though part of me does miss the feel of physical faders under my fingers...I'm more concerned about sound quality, specifically the relative accuracy/robustness of mixing algorithms in DP versus those in a digital board, versus the summing circuitry in an analog board. What mixing method gives the best clarity, detail, low-end solidity, imaging, and headroom?...he wondered.

Sound quality comes from the gear you have..As I stated before that if you keep it in the digital realm it's going to stay digital. If you bring out analog and put it in an analog board it will stay with that warm analog sound(sort of!!) Also depends on your listening setup..what speakers and amps you have helps in that department as well. Everyone has their own interpretation of what sounds better but to be honest that's their ears..not yours.
As far as the algorithms in DP vs a digital or analog board..that's really not pertinent. What is pertinent is your audio hardware and how well it sounds going in and out. Yes the software can lend a hand but if the software get crap..well, crap in means crap out!
I enjoy mixing from my software..I use Nuendo but have frequently used DP and it sounds great! Just remember that it's your ears that are tuned to a certain sound..try and match "that" sound as best as you can
Opus

After audio is recorded to your HD leaving the box to mix through a digital or analog mixer then go back in is not a good idea IMHO.
Using a mixer/surface controller for a "hands on" feel is a better way to go. Of course, routing tracks out and in to new tracks is cool if your adding effects and other goodies provided you have good A/D/AC's.
Since sound is your priority here I sugest the best time to leave the box is at the end of your project and even then 24 bit data files to be mastered are the way to go. ;)