Trouble with a hardtail is that most punters who aren't used to the alps will find it much much harder on their bodies – it just is. On the Singletrack reader week last year we had a couple of hardtails on offer to ride, for free I might add, and how many people rode them? Just me and Benji. Everyone else was enjoying the full suss offerings too much.
We also ran a Chameleon as a hire bike a few years back – again, just myself and one guest rode it all summer long – and he ended up buying it at the end. If you're the sort of person who wants to ride a hard tail in the alps, then you're most likely to have brought it with you.
Nothing against hardtails – I ride one here in Morzine and around the alps frequently, I love it. Zero point in them as hire bikes though.
My personal full sus is a Nomad, 170mm lyrics, coil shock, 2.5 tyres, single chain ring. In my opinion it's just about the best bike for riding around the alps – long singletrack descents, short climbs, chairlifts etc. Then if I'm feeling the need for some punishment I get the ragley out.