We elucidate the relationship between Schrodinger-cat-like macroscopicity and geometric entanglement, and argue that these quantities are not interchangeable. While both properties are lost due to decoherence, we show that macroscopicity is rare in u
niform and in so-called random physical ensembles of pure quantum states, despite possibly large geometric entanglement. In contrast, permutation-symmetric pure states feature rather low geometric entanglement and strong and robust macroscopicity.
