I've been (2008) and had a great time. I haven't been to MHSSC but can make a few guesses about the differences based on their website.
First off; age. The British freeski camps have a much larger/older range of people. There are quite a lot of adults at the British camp. The biggest group of people at the BFS were either 16-21 but there was about as many people who were 25-35. There were a couple of younger teenagers and one kid who was about 10 I think. By the look of it, MHSSC is full of younger kids. As the BFS camps are full of a) adults and b) Brits there is quite a lot of drinking and going out. I think the drinking age is 16 in Switzerland and it didn't seem a problem for the older kids to go to the bar.
Ability; there is a big range at the BFS camp. The ability seemed separated into two groups, those just learning park (i.e. 3's) and those trying bigger off-axis/inverted spins with grabs; there weren't that many people in between the two but this might have changed as I know that quite a lot of the people who were just learning park two years ago got really into it and kept going back so the overall standard's probably improved. When I was, there everyone who wanted to learn 3's had them nailed by the third day and then had to figure out what to learn next. I don't know about the ability range at MHSSC.
Terrain; the BFS camp technically uses a public park. But there is hardly anyone else there apart from a Scandi snowboard camp and it never seemed busy. When I went there was a pipe (I'd guess at a bit less than an 18' pipe but definitely bigger than a 15" pipe), and a three jump main line. The pipe in the MHSSC camp vid clip looks pretty beat up and not nearly as nice as The BFS one. The bottom jump had two kickers, one big one small. I'd guess the small one at 30 feet, the bigger one at 40 feet. The middle jump was the biggest (about 50-60 feet). There were also a bunch of small jumps in a line. There weren't that many boxes/rails (four boxes and a couple of rails I think).
Accommodation; The BFS camp is in a different league to the MHSSC camp. Its also better than COS's accommodation and the only thing comparable is Momentum's accommodation.The hotel the BFS camp used was really nice. You'll either have your own room (with a shower), share a large double (with a bathroom) or possibly share a really large triple (these had bathrooms and kitchenettes). The rooms have TV, hi-fi and Playstations. The hotel itself is really nice, has a chilled cocktail bar and there is also a bar/club in it called Popcorn which is bar far the best place to be in Saas-Fee at night.
Coaching; I had coaches who great on the snow and in the bars. I had a guy called Pat Sharples (Salomon UK team manager and runner of the 'grom camps' in the UK) pretty much full time. James 'Woodsy' Woods and Paddy Graham also spent a lot of time with my group helping Pat. Woodsy was injured and not jumping but was great to have around helping, his enthusiasm is infectious! Paddy's also great as a coach and always seemed happy to explain and demonstrate any trick I was working on. The other coaches were all a chill bunch of lads. There was video review every day.
Activities; the afternoon activities at the BFS camp will be more limited than at Hood. There's a trampoline, football (or soccer if you're a Yank/Cannuck), skateboarding, miny golf and a high wire course (with a zipline over a massive gorge which is spectacular). You can also rent a bike (but all the rentals are a POS) or go for a hike if you want. I liked the fact that the trampoline was set up next to Popcorn (the bar/club)!
Other; The weather at the BFS camps is normally amazing or terrible, it never seemed anywhere in between. Most days were bluebird but the bad days are so bad that you can't go up to the glacier. As a result the 'off' days are flexible. If its good, you ski; if its not, you don't. If you went out drinking heavily the night before the next day will be sunny. If you stayed in and went to bed then the next day will be terrible.