I subscribe to all three. Here is my ranking:
1. International Bonsai Magazine:
http://www.internationalbonsai.com/page/1403493
Great mix of Japanese translations and American articles; excellent photography, some pots discussion, and usually themed toward a style or species...though not so much so that its exclusive if the theme isn't your preference. Plus, Bill is an incredible ambassador for bonsai in the USA, generous with shows, material, and contributions here. Gwwrood to support his efforts wherever possible.
2. Bonsai Today is defunct, but Bonsai Focus is a European publication that seems to feature less and less Japanese translations, and more European styling articles, good galleries, and some discussion on pottery. Still very well-done, but with a much different flavor than Bonsai Today had.
3. The Journal of the American Bonsai Society is good too, but IMO, the most expensive relative to the content and quality.