It's actually a stylistic difference. Academically, Beethoven is considered classical so ornaments should be played in the classical manner. Thus, the beginning note of the ornaments fall ON the beat. It's kinda like the Mozart Turkish March. No on plays the grace not before the beat, although that's how they are written. It's because stylistically, ornaments fall on the beat in the baroque and classical era. I'm not sure why older pianists (Horowitz, Rubinstein, etc.) tend to play all of their ornaments romantically (beginning of ornaments fall before the beat).
However, there ARE exceptions. Sometimes the other way just sounds better both in classical and romantic music.