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I am an old f**t.  I personally use both depending on the situation and
which code or standard I'm using. They are simply alternate methods of
communicating the results, a language if you will. I don't see a particular
advantage of one over the other.  The important thing is not whether we have
one safety factor or a dozen.  Rather, it is how well do we understand the
actual behavior of the structure.  
Roger appropriately points out that serviceability issues often dominate the
behavior we are trying to achieve.  I have to laugh when I see the
pronouncements about how much more accurate LRFD is than ASD and how "we"
can understand the structure so much better. When you start from the same
basis, i.e., linear elastic analysis, you have the same inherent "grossness"
to the results. It really doesn't matter whether you amplify the loads and
factor the material capacities or use allowable properties, they still
represent elastic behavior.  And it still is only a MODEL of the structure.
I've also done enough non-linear work and comparisons to observed behavior
to know that the linear elastic answers, regardless of how they are scaled,
are simply a ROUGH model of what the structure will do.  Even the non-linear
analyses are not exact.  They usually represent a closer approximation but
don't always give good results.  
A particular example is in SMRF joints. Many types of analyses have been
done assuming great ductility based on very limited early research work by
Popov as well as allowable stress design using allowable stresses.  The
Northridge earthquake gave us a reality check and a wake up call.  In spite
of the level of sophistication of the analyses, in spite of whether we used
LRFD or ASD, joints failed in much larger numbers than we would like.  The
joints didn't really care how we analyzed them.  Whether "factored" or
"allowable" values were used was essentially immaterial because we, as a
profession, had the model wrong. We didn't include the possibility of joint
fracture. Luckily, buildings didn't collapse in that earthquake due to those
failures (for a variety of reasons such as short duration, redundancy, etc.)
but there was great economic loss.
I think the current emphasis of the 1997 UBC earthquake provisions on
visualizing the behavior when large inelastic actions occur is far more
important than whether ASD or LRFD is used as the analysis technique.  The
precision of the "answers" as we know them in seismic design must always be
kept in mind.  I'm reminded of a quote by Jim Amrhein that "we should not be
so precise that we forget to be accurate."  Accuracy means knowing the
limitations of our models and not attempting to push them to a degree of
precision beyond what they can realistically tell us.  For actions such as
dead loads and live loads, substantial research is available to get a good
handle on the variance of these loads.  For wind and seismic loads, much
less is known.  To push a seismic or wind load design to the "minimum" code
requirement is stupidity.  Mother Nature reminds us with each succeeding
earthquake, tornado or hurricane how little we really know about these
events and their effect on our structures.
I'm old enough to remember when USD was first being introduced.  The
operative argument in favor of USD was that the answers were really about
the same as WSD because USD was "calibrated" so that would be true.  From
the work I've done with LRFD, the same seems to be true even if it isn't as
blatantly stated.  We must remember that whatever method we use is simply a
model of the real structure.  Predicting and providing for the structure's
actual behavior is what is important.  ASD and LRFD are simply tools that
help us to make decisions.
Bill Cain, SE
Oakland, CA