I'm not sure how similar they are. I believe that the London and Edinburgh rides both had the route agreed and published some time in advance, and there was involvement from The Times newspaper. Road closures were effected by the police for the London ride, which seems to have enabled a safe protest. Critical Mass rides seem to be rather more fluid and informal in their organisation- do the local police close the roads for riders, and are they enabled/sponsored by businesses? I'm not entirely sure of how far the Times were involved with the UK rides but there was definitely some involvement.
The Times is currently spearheading a huge campaign for improving cycling safety in the UK. There's been a lot of news about cycling over the last few weeks and it would be great if we actually saw some positive changes come about.