Howdy Seth,
the wire springs tend to be a little weaker and don't have the "snap" that the flat springs have, plus they tend to get a little weaker over time. This can aggravate over-rotation problems with fast and hard cocking. Duelist style shooters would be less likely to have problems than traditional style two handed shooters. And while the Italian flat trigger/bolt springs are definitely the most likely item to break in any Italian gun, the aftermarket flat springs seem to be well made and reliable.
Having said that, my first (of four) 1851 Richards-Masons has a wire trigger/bolt spring that was made from piano wire by the late Bob Taylor which has never caused any timing problems and I shot that gun traditional style a lot. But he might have made it from a stiffer wire than commercially available wire springs, I don't know.