I've really enjoyed reading this discussion so far and, as I attended both schools, thought I'd contribute.
I attended HVC between 11-16 and it's absolutely true that there is a more 'relaxed' atmosphere there compared with LMS. HVC is 1/3 the size of LMS with obvious consequences.
It's a great school with a 'sunny' outlook on life but can feel somewhat claustrophobic when you reach the 4th and 5th year due to the smaller number of pupils and the fact that everyone seems to know everyone else's business.
I've seen it mentioned in previous posts that there is a distinct attitude difference between HVC and LMS. This is true, LMS has a 450 year history and more traditional stance which inevitably generates a more classic schooling outlook.
In my experience, whilst there is a small amount of snobbery between the 2 schools, some HVC students positively revelled in being the 'underdog' and didn't see the situation objectively.
What it came down to, as with most situations was that if you met students from LMS as a HVC student with a chip on your shoulder you wouldn't get very far and you'd see what you expected to.
I had no trouble whatsover.
I attended LMS for 6th form and didn't find it oppressive or old-fashioned. It has a strong sense of tradition but, as noted previously, it's rightly proud of it's 450yr heritage.
I found the more traditional approach benefited me while I was doing my A levels as the work load was so heavy that having a strong teaching presence kept me on the straight and narrow.
The teachers definitely do not spend more time chasing people for their uniform infringements and the teaching staff I came into contact with (History, English sociology and maths depts) were brilliant - committed, enthusiastic and willing to help those who were struggling.
I also grew up in Eyam so I hope you enjoy living there as I have loads of happy memories from the carnival, village show and pantomime!