They are both delicious, but salsify (the vegetable oyster) definitely has the better flavour, as well as being easier to prepare (scorzerona has black roots and is an absolute nightmare to peel. The roots of both need a drop of vinegar or lemon juice in the water to stop them going black (it`s the iron in them).
Both can be left in the ground until required. Personally I prefer salsify peeled, cut into thick slices, parboiled and smothered with butter, but if you like something a bit more intricate try this:-
Parboil the sliced roots and then place in a pyrex dish, use some of the parboiling water to make a white sauce, cover the roots with it, add breadcrumbs and grated cheese on top, then bake in hot oven until nicely browned.
If you leave some salsify roots in the ground until spring they will sprout again - use the sprouts at about 4inches long for salads, and up to 8 or 9 inches long to cook as an aspasagus-tasting spinach.
