My experience loosely matches Richard's, certainly
in terms of wanting to think that -qreg- is as good
because of the much greater ease in explaining it.
At the same time, if you have outliers everywhere,
you are possibly working on inappropriate scales
and should wonder about reaching for a transformation
or, in some frameworks, a different link function.
My inclination would be to stress that either program should probably be a
last resort, rather than a first. Outlier problems are often just a result
of coding errors, e.g. you left a zero out, or you didn't handle missing
data codes right. Or, the problem may be model specification: add another
variable or two and maybe the outlier isn't such an outlier any more. I
preach similar things with regards to heteroskedasticity. Don't just
immediately jump to WLS or something like that. Subgroup differences in
variable effects might produce a pattern of heteroskedacity, but adding
interaction terms may make that go away.
