Assuming that the pianist has many strengths and has a large potential to display more than one kind of playing, I'd like to hear pieces which represent different qualities. Overall, I'd be keyed into tonal pallets and emotional depth and would hope that each selection lends itself appropriately to some adequate form of that, but to get a good sense of a pianist's musicianship I'd like to hear a piece for each of following characteristics:
1. Slow and song-like
2. Physical power and stamina
3. Contrapuntal Thinking
(4. Agility) -- not necessarily less important, but since it's just supposed to be 3, I'd choose it last.
I can't say that I have a sense of ideal pieces for these quite yet, except for I'd like to hear something by Bach for number 3.
For the first one, I think this ends up saying almost the most about a person, about pianism, and musicianship. To be able to suspend tones with interest, to be able to continue slower phrases without losing the line, these require a particular musical maturity, a particular musical interest on the part of the pianist's, and a certain knowledge or instinct about resonance.
For the second, aside from the fact that I'd like to hear the pianist's "inner roar," I'd also like to hear if/how a pianist can do this without it being a slap. Like it just comes from deep within.
For the third, I think that this shows a very certain kind of intelligence in being able to maintain the individual musical characteristics of each line, while using the piano's tonal abilities to have these come to life, and then how to have all of this tie together to form the overall tapestry.
The fourth ... well, it can be fun, it can be kind of like lightening, but I'm especially fond of it within a musical context, particularly when its presence expresses something musically where the concept is unequaled at a slower tempo.