Barring discard attacks and trash for benefit or multi-Prince shenanigans, princing a Scheme is strictly better than princing a Smithy because you can always at least Scheme the Smithy and play it as your first action each turn, which is functionally equivalent to princing a Smithy, but you can also choose to play something else first (say, Fishing Village - Watchtower) or scheme another card this turn. Hence a princed Scheme gives you greater flexibility.
There are enough cases where you want to prince the Smithy anyway, though. E.g. if you've princed another card that you sometimes want to play after the Smithy, the already mentioned discard attacks and maybe some specific TfB spots.