Use of snares, of any kind, should be made illegal. There is really no good reason for their continued use in this day and age, in my opinion.I imagine that a fox probably does feel some pain when it is caught, however to me this would be preferable to being shot in the leg and dieing of septecimia or being caught in a snare for 24 hours (the legal requirement to check a snare is 24 hours). I really do think that although these things are not nice they are a fact of life, things do die and often not in an awfully nice way.
http://www.woodland-trust.org.uk/campaigns/briefingsmore/snares.htm