As someone said earlier, a very interesting thread. We still use an analog board at our church for recording (an Allen and Health GL2200). The setup has two effects patched in, reverb and chorus and patched back into the main mix. It then goes to a stereo compressor, followed by a 31-band EQ and then onto a CD. Everything is recorded in real time.
What I have found is that the analog recording allows you to get away with stuff that you simply can't get away with in the digital realm. Gain is the main culprit here, as when I go over 0 db on a digital board it is clip city, but that is not a problem with the analog board. The other thing is that everything is recorded at once and exported to a 2-track 'stereo' CD. So the process is quicker (as someone alluded to earlier), but there are no do-overs. Forget to unmute a channel on a guitar solo and your stuck - you can't get it back. You also seem to be 'chasing' stuff at times. Digital onto multiple tracks and you can fix to your hearts content, but it will take considerably longer. Multiple tracks on tape and you loose quality each time you redo it, no loss when in digital.
In the end I think each has its positives and negatives. The key is to find what works for you. And as Yorolpal so rightly pointed out, in the end its not the gear but the gear-head and the talent that really matters. I tell my guys we have better equipment than the Beatles had when they recorded Abbey Road. If you don't get a good mix, don't blame the equipment!