Based on the the London Analysis of Police Collision Files (2007-2011) 2% of serious P/C (Pedal Cycle) accidents are caused by a right cross (what would be a left cross in the US). I think this is the only type of accident that one could legitimately claim could be avoided with the aid of a blinking headlight. Alternatively, the cyclist could slow down or stop to avoid crashing head-on into a motor vehicle, which I think is what most people do.

By far the most common serious accident between a motor vehicle and a bicycle in the study mentioned above is the left hook (what would be a right hook in the US) at 32%. This is also the easiest accident to avoid by not passing cars on the right (or the left in the UK). The second most common accident at 17% is the other vehicle running into the the rear of the P/C. I haven't seen the data but have to believe that both of these types of accidents (which comprise almost half of all serious P/C accidents) are pretty unusual for motorcycles.

I wouldn't be surprised if a left cross is the most common motorcycle accident. The obvious difference is that even in urban settings motorcycles are travelling much faster than bikes and have significantly increased stopping distances making these types of accidents harder for the rider to avoid.