Pieces good for competition are ones which show lots of elements of the piano. How the piano can be used to make different sounds, the effective demonstration of the different sounds the piano can go through on stage is really what will win you a competition. So playing a piece which has a lot of content that highlights a lot of what the piano is capable of is good. That could include a whole huge repetiore of virtuosic pieces from the piano composers like Liszt, Chopin, Scriabin, Rachmaninov etc who really know the capabilities of the instrument. So I think you shouldn't play anything in the classical or baroque (some exceptions, eg: impressive Beethoven Sonata) if the choice of what you play is totally open, play more romantic, 20th/21st.
The earlier piano works do not really bring forth all that the piano can do. It is like the olympics sports i guess. Does a diver for instance go do a safe dive, something traditional and routine and get good marks, or do they take risks and push the limitation of their physical ability to get the top marks? Piano competitions are exactly the same but based on the choice of music, what you play you must be convinced is going to excite anyone who hears it. What you have must push the limits of yourself to demonstrate the acrobatic nature of your piano dive lol.
Of course the traditional methods win too, but it depends on what the competition specifies, but if it is an open choice then I would really go for the works after the classical.
As for performance programme I think what is critical is that each piece gels with one another, so that when you talk about your music to your audience you are keeping a solid image not just jumping all around the place. For instance i would find it hard to start talking about Gottschalk, an American pianist and composer then all of a sudden after him start talking about Bach, or vice versa. The connection isn't there. So if pieces paint similar images, or have similar ideas than the other, they could be coupled together, not only for sound logic but also the logic in your talk presentation to your audience. This logic can often be found just by trying to gather as much info as you can on the pieces you want to play, the order reveals itself to you then and sometimes even what needs to be removed and replaced.