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1D III is certainly a fantastic camera and the battery life is simply amazing, as in you easily get 2000+ shots, maybe 3000 shots. IQ is excellent for 10MP.
I would pick the 1D III over the 7D mk I (I owned both) if forced to choose just one (but I think 7D is a great camera), but I would think the 7D II would be a better camera if it eventuates, but it'll be a fair bit more expensive and how long are you prepared to wait
However if you own a 5D III, that provides more reach than 1D III if FL limited, ~ 16%, has even better AF, better IQ (especially if not FL limited and at high ISO). The 1D III will provide better fps and battery and build, but otherwise 5D III is a better camera. Personally the best partner for the 5D III is the 1D IV or a 7D, but I know you don't think much of the 7D and 1D IV is simlar price to 5D III. If MP don't matter and you really would like the extra speed and responsiveness then at the current prices the 1D III is an awesome buy IMO.