If you need the extra burst then 7D or 1DIV would be the way to go. If you don't then the 5DIII is really a great camera.
I bought one to go with my 1DIV for shooting wildlife (Birds in flight + Static), landscapes and real estate commercially. The details are so much nicer then my 1DIV especially at higher ISO (Over 1250) that I ended up selling my 1DIV and picked up a second 5DIII body.
If its all about the burst rate then your question is easy to answer. If other factors weigh in then it opens up your options a bit. Considering that you are coming off of 3.4FPS then the 5DIII at 6FPS will feel like a machine gun, however it is a far cry from 10FPS of the 1DIV.
Good luck and happy shooting,