In reply to ceri:
I've generally worn 3 season leather or fabric/goretex boots for via ferrata - but then, we usually seem to have managed to hit coldish weather and a fair amount of snow & ice. Indeed, on some of the routes the wire was covered in a thin layer of ice, along with the rock, which made life more entertaining. If the weather had been warmer, as suspect I'd have worn approach shoes or trainers.
I wouldn't have thought your footwear's going to be a limiting factor, even on the harder via ferrata, so whatever you most comfortable in for the approaches (which can include a lot of scree) is probably best.