I don't think that their is any statistical evidence in favor of either procedure.
Both are flawed if the procedure is not flown correctly.
In the UK over the numbers means - over the numbers
In the US intercept at 45 degrees means - intercept at 45 degrees.
Making up your own joining procedure in either country, in a busy circuit, with all the lookout in the world, will not stop this happening again.
Maybe, a N reg parachute
will be mandatory next, along with Mode S and 8.33kz spacing.