There are many species of Sempervivum (Hens and Chicks), and each may have a different edibility status. However, Sempervivum tectorum is edible. That appears to be the same kind you have, but I don't know. They're called Common Houseleeks for a reason.
Ours appears to be S. tectorum, and I've eaten lots of it without any toxic symptoms whatsoever. I've even sliced it on pizza. The taste varies from sour (like an unripe apple) to highly astringent. I like it fresh or cooked. It's refreshing fresh, I think. Despite what my link above says, the taste and texture of the new and mature leaves is exactly the same, in my opinion, and I would think, the edibility, too. I've primarily eaten full-sized leaves, as they make an easier meal than the small ones. Very old, mature leaves also taste similar, but may be softer and seem faded. I also don't think they taste anything like cucumbers.