If I get your questions right, it is that it all depends. As far as a digital mixer going to SONAR, all the above listed act as your AD/DA via FW etc. So your recording signal would go through the mixer w/ EQ and effects and get laid down in SONAR.
The mixers are different, however. The A&H is an analog mixer w/ a ADDA tacked on. So you get a nice analog EQ going in, but I don't think it includes any digital time based effects (reverb, etc.) It will also act as a control surface for SONAR - it has two different modes (analog and digital). I don't know how well the other two digitial mixers work w/ SONAR. But you should be able to re-record them w/ the mixer effects or use the mixer to add reverb etc. during mixdown since it all takes place in the world of digital.
Again, the A&H is different. You take your digital audio from SONAR (with all the in the box effects you want from SONAR) and pass it out as separate tracks or stems to be eq'ed and summed by the analog mixer. You can, of course, use your analog hardware w/ it on mixdown (or recording), just like a regular mixer.
Hope this helps. If it was me, I'd take the A&H any day. You can even add your own convertors, I believe, via ADAT, although there are some mixing restrictions as I recall. But basically, it is an analog mixer while the others are digital.
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post edited by AT - 2011/06/07 13:28:58