Hi there.
I was admitted to both of these programs, although I won't be attending either. Couple of points from my end:
HEC seem to care about their students quiet a lot (good interview process, good scholarship money, good communication), but the career opportunities seem to benefit those with French or looking to stay in France. That is not hard and fast, obviously, as many do end up in London. That said, if London is the goal, I think the networking and location that come with LSE would be hard to beat.
LSE's whole process seemed quite informal to me (no interview, little communication), but they do seem to pull together a solid cohort. I am in the admitted students FB group and its a diverse (across Europe, mostly) bunch with strong backgrounds and even stronger goals. I was impressed by the introductions people were posting (more so than those at MIT, even), but that is just a little bit of anecdotal evidence.
No real wrong decision here I reckon. Good luck!