5DMK3 since you don't have any problem regarding the lens focal length but is having problem with ISO. 5D3 is better in ISO performance than 1DSMK3 by at least one or two stops. 1D4 is much worse than 1DSMK3 in ISO performance.
Don't know what camera you're looking at, but the 1D IV is superior to the 1Ds III in ISO performance.
I'd honestly go for the 1D IV. Considering that you're used to a 1D style body too.
But for sports- 10 fps? great ISO performance? 1.3x crop factor? superior build? Yes x1000000.
I'd go for a 1D IV over a 5D III in your purpose.
Shoot me if you will, but I sometimes feel as if I should trade my 5D III for a 1D IV, but I tend to work with landscapes more so I wouldn't.
It would be good to have that old flagship combo of a 1D IV and 1Ds III.