It depends on the quality of the pres in the mixer vs the quality of any external stand-alone pres a studio might have. Track with whatever gets the job done the best.
If you have a cheap mixer almost any stand-alone pre [ even inexpensive ones ] are going to give you better performance.
It's also common to use the mixer for monitoring only and to completely bypass it during tracking - by going straight in mic/pre/compressor/recorder. A lot less wire doing it that way = a lot less noise on each track.
If your using something like a Soundcraft M series or Ghost then you can get good results with those pres and make some nice tracks. If your using a Behringer then out board pres would be a great improvment.
i tend to agree. when tracking a band live, i tend to use my Mackie24*4's pres for the bulk of things simply b/c i've got a limited amount of outboard......but snare and kick (or keeper "live" vocals, if/when applicable) go into the 528 or VTB1 just b/c they're "meatier" sounding.
you'll sometimes find it helps to use a "channel strip" for vocals, since you've typically got a compressor and eq self-contained within the unit just b/c it's a little more convenient (IMO). and lord knows i'm a creature of convenience.
i DO tend, though, to use different mics and pres for lead versus backing vocals. you want the lead vocals to sit forward a little more than the backing ones, and that's most easily addressed (on the engineering side) with careful selection of mic and pre.