I've never been to Alagna, but I've been to Corvara in Badia (near Val Gardena), and there is some really awesome backcountry terrain of the top of the Sella Group (Gruppa di Sella in italien, or Sellagruppe in german). If you get a chance, check out the "Val di Mezdi" aka "Mittagstal" which means "Valley of Noon." It runs 5,300' down from the top of Piz Boé (3343m) to Corvara.
It starts out with some steep snowfields on the summit cone of Piz Boé (pronounced pizz bo-eh), funneling into a tough little chute, and then opening onto the flat plateau. From the Plateau there are two main routes into the valley itself. skier's left is the easier of the two, a narrow couloir at about 45°. The other entrance (skier's right) is a little longer and a little steeper (I wanna say like 45°-50°), but both funnel into this long hanging valley.
The Valley floor is littered with large glacial erratic boulders which are good for airtime if there's a lot of snow. At the end of the valley the bottom drops out and you ski down the steep (45°) streambed to the bottom, where lifts can take you left (Val Gardena) or right (back to Corvara).
If you decide to go. Stay at the Hotel Col Alto in Corvara. It's the best food I've ever tasted.