Polycarbonate is much stronger. It will not break easily, even if someone hits it hard. That makes it good for busy places like schools, subways, or outdoor bus stops. However, polycarbonate scratches faster and becomes foggy over time. It also costs more.
From my experience in the display industry, many people buy polycarbonate thinking it is always better because it is “strong”. But for most indoor retail or home displays, acrylic is the smarter pick. It gives you a premium look without the high cost. Only choose polycarbonate if you really worry about strong impacts or vandalism.
So ask yourself: will your display face heavy traffic or possible hits? If yes, go with polycarbonate. If not, save money and get a better look with acrylic.