Aw crumbs - I've just done a massive critique on both schools and areas then realised I have to join first - have lost all. Never mind here we go again!
I live in HV and have two primary aged children, so hear all the gossip about the schools, HVC and LM included. Hope Valley is very beautiful - rugged hills great for mountain bikers, climbers, walkers and parascenders/hangliders etc - perfect for outdoorsy people but you won't feel like an alien if you're not! Lots of commuters to Sheffield and I believe Hathersage has the highest % of anaethetists and surgeons in the country (or something like that) HV consists of a number of villages (Eyam included). Bakewell is a town rather than a village - very beautiful, more rolling countryside with Chatsworth just a mile or two away. Has a good percentage of upper middle class people and if you're a yummy mummy you wouldn't be out of place. Lots of independent expensive shops in Bakewell.
Both places are expensive to buy houses but now is the time to buy with prices being a lot lower now than they have been.
LM school had a god like status when we first moved to the Peak District - I think that reputation has gone downhill over the last 5 years while HVC has gone from strength to strength. I heard that 47% of the current Y7s were from outside of the catchment area! Sounds huge doesn't it - probably because they had small year groups coming in from the village schools?
LM has very good and extensive sporting facilities whereas HVC has something to be desired HOWEVER, they do seem to have very good teams in the standard sports - netball, rugby etc - I don;t know about LM but I guess they'd be pretty strong too as the school has 1600 pupils or thereabouts, HVC with just 5 or 600.
HVC has an amazing reputation for music and the arts which I always think is funny as its so good with its technical subjects rather than academic. It puts on amazing presentations, the last one being Les Mis which blew me away, I couldn't believe I was watching 14 and 15 year olds, it was like a west end show! The singing was so professional. Their woodwind ensemble is very popular and not just for the geeks - it is seen as being really cool to be in it!
HVC might be better for younger children as it is so much smaller than LM, mind you they still think it is massive compared to the village schools!
One downer against HVC which personally I'm not too sure about but I know it bugs the hell out of a lot of parents, is the lack of uniform and the generally slovenly look of the kids. The head has a very laissez-faire approach and the kids are given a lot of choices and responsibility whereas LM has strict uniform and I think suits academics and "yes sir" kids. I think LM gives a lot better impression if you are looking around but don't be too taken in as I've heard it has had quite a drugs problem. I'm sure HVC has it as well, but I haven't heard the stories like I've heard about LM.
Hope this helps with your choices - if you visit the schools make sure you talk to the kids there too.