We thought Bier’s points were reasonable, so we tried to replicate his approach. We looked at the raw violent crime numbers for each country, using statistics for England and Wales for 2012 and for the United States for 2011, in a way that sought to compare apples to apples. (We should note that the United Kingdom includes Scotland and Northern Ireland, but the numbers in the meme appear to be based only on crime in England and Wales, which are calculated separately.)
For England and Wales, we added together three crime categories: "violence against the person, with injury," "most serious sexual crime," and "robbery." This produced a rate of 775 violent crimes per 100,000 people.
For the United States, we used the FBI’s four standard categories for violent crime that Bier cited. We came up with a rate of 383 violent crimes per 100,000 people.