It's not about E major as such -- all the songs were transposed to C major/A minor scales. It's about chord III in major scale or chord V in minor scale. In classical music chord III is basically never used in compositions in major keys. In minor key music, chord V is typically altered to major as it leads to the tonic much better. Often, for instance, melody ends in G# and A. Minor V, on the other hand, is kind of ambiguous and rarely, if ever, used.

EDIT: Thinking about it, E minor is fairly common in phrygian scale (it's the tonic chord), however, phrygian, unlike dorian or myxolidian, which are used at least sometimes, is super rare -- its dominant chord, B dim, is dissonant, which kind of sucks.