This is a pretty broad question, but in general I think a score is going to be preferred over a lead sheet in almost all situations. In particular, a well-arranged piano score and NOT a PC score most of the time, as many PC scores try to jam in as much information about the orchestration and are extremely difficult to sight read.
The reason is that, short of extremely high-quality professional theater companies that can afford to hire the best accompanists in the city, accompanists are going to vary in quality dramatically. A student theater group is going to use whoever is willing, and they commonly end up with someone who isn't very good. Community and semi-pro companies tend to have reasonably skilled pianists, but they may not be completely rounded. A lead sheet is worthless to someone without the training/experience to read one--a classically trained pianist can't do anything with it. And even for someone with some skill in this area, a lead sheet still presents a lot of challenge if they're not familiar with the piece. Really, lead sheets are a good notational system for something that's going to be rehearsed, but where you want to be vague enough to get out of the performer's way. An audition is a sightread.
A score is at least providing notes that can be played, and a decently experienced musical theater accompanist should know how to fake through one if it's not easy enough to be totally sight read, even if their sheer technique is lacking.
I might expect to see auditioners to show up with lead sheets for a rock musical, but I would certainly ask first if this would be acceptable and be prepared for a "no".
He also suggests that an auditioning singer will be considered better prepared if they have score than a lead sheet.
My initial reaction to this was "no, that's not necessarily true", but when I thought back to the times that people have brought me lead sheets, I've invariably gotten the impression that they weren't well prepared. I think it's primarily other factors with the lead sheet being only a consequence (specifically, I usually get the impression that the auditioner is only using that song because it's the only song they know, and that this crappy lead sheet is the only thing they could whip up), so if you can be professional about it you should be able to avoid that.
All of that being said, most accompanists will greatly appreciate a score with chord symbols, since the aforementioned faking is based on doing an on-the-fly harmonic analysis and re-realizing the music in a simpler way, and having the chord symbols eliminates a lot of the mental work.