If you reverse a classical guitar then the strings are the wrong way round, reverse them and it will sound rubbish as the top thicknessing and bracing are set up for different properties and tensions of the bass and treble strings.
I was sceptical about this because lots of guitarists/bassists labour under the misconception that lower/heavier strings are higher tension when the reverse is usually the case. Anyway, it seems that classical guitars are usually symmetrically braced so ideal for reversing should you want to.